{"id":155322,"date":"2022-03-26T00:31:03","date_gmt":"2022-03-25T19:01:03","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/fibonacci-sequence-explanation-formula-list-types-origins-and-faqs\/"},"modified":"2024-08-29T12:40:27","modified_gmt":"2024-08-29T07:10:27","slug":"fibonacci-sequence-explanation-formula-list-types-origins-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/","title":{"rendered":"Fibonacci Sequence"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Fibonacci_Sequence_Meaning\" title=\"Fibonacci Sequence Meaning \">Fibonacci Sequence Meaning <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Fibonacci_Sequence_List\" title=\"Fibonacci Sequence List \">Fibonacci Sequence List <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Fibonacci_Sequence_History\" title=\"Fibonacci Sequence History\">Fibonacci Sequence History<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Fibonacci_Sequence_Spiral\" title=\"Fibonacci Sequence Spiral\">Fibonacci Sequence Spiral<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#How_to_Draw_a_Fibonacci_Sequence_Spiral\" title=\"How to Draw a Fibonacci Sequence Spiral\">How to Draw a Fibonacci Sequence Spiral<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Fibonacci_Sequence_Formula\" title=\"Fibonacci Sequence Formula \">Fibonacci Sequence Formula <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Fibonacci_Sequence_Properties\" title=\"Fibonacci Sequence Properties\">Fibonacci Sequence Properties<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#1_Connection_to_the_Golden_Ratio\" title=\"1. Connection to the Golden Ratio\">1. Connection to the Golden Ratio<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#2_Ratio_of_Successive_Fibonacci_Numbers\" title=\"2. Ratio of Successive Fibonacci Numbers\">2. Ratio of Successive Fibonacci Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#3_Patterns_in_Multiples\" title=\"3. Patterns in Multiples\">3. Patterns in Multiples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#4_Fibonacci_Sequence_Below_Zero\" title=\"4. Fibonacci Sequence Below Zero\">4. Fibonacci Sequence Below Zero<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#5_Sum_of_Fibonacci_Numbers\" title=\"5. Sum of Fibonacci Numbers\">5. Sum of Fibonacci Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#6_Connections_to_Other_Mathematical_Concepts\" title=\"6. Connections to Other Mathematical Concepts\">6. Connections to Other Mathematical Concepts<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Fibonacci_Sequence_in_Real_Life\" title=\"Fibonacci Sequence in Real Life \">Fibonacci Sequence in Real Life <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Fibonacci_Sequence_FAQs\" title=\"Fibonacci Sequence: FAQs \">Fibonacci Sequence: FAQs <\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#What_is_the_Fibonacci_Sequence\" title=\"What is the Fibonacci Sequence?\">What is the Fibonacci Sequence?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#Why_is_the_Fibonacci_Sequence_Significant\" title=\"Why is the Fibonacci Sequence Significant?\">Why is the Fibonacci Sequence Significant?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#What_Are_the_First_10_Fibonacci_Numbers\" title=\"What Are the First 10 Fibonacci Numbers?\">What Are the First 10 Fibonacci Numbers?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#What_Is_the_Value_of_the_Golden_Ratio\" title=\"What Is the Value of the Golden Ratio?\">What Is the Value of the Golden Ratio?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span style=\"font-weight: 400;\">The Fibonacci Sequence is a series of numbers that begins with 0 and 1. Each number that follows in this series is the sum of the two numbers before it. The sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and continues indefinitely. In this article, we will discuss the Fibonacci Sequence in more detail. <\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check:<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/faces-edges-and-vertices\/\"> Vertices, Faces and Edges<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-731109\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52.png\" alt=\"Fibonacci Sequence\" width=\"1640\" height=\"924\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52.png 1640w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52-300x169.png 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52-1024x577.png 1024w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52-768x433.png 768w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52-1536x865.png 1536w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52-150x85.png 150w\" sizes=\"(max-width: 1640px) 100vw, 1640px\" \/><\/p>\n<h2><span style=\"font-weight: 400;\">Fibonacci Sequence Meaning <\/span><\/h2>\n<p><span style=\"font-weight: 400;\">The Fibonacci sequence is defined as a unique series of numbers that starts with 0 and 1. In these sequences, each following number is the sum of the two preceding ones. The Fibonacci sequence is like: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. Each number in this series is referred to as a Fibonacci number, and the first two terms are 0 and 1. The below given formula can define the Fibonacci sequence: <\/span><\/p>\n<p><i><span style=\"font-weight: 400;\">F<\/span><\/i><i><span style=\"font-weight: 400;\">n<\/span><\/i><i><span style=\"font-weight: 400;\"> = F<\/span><\/i><i><span style=\"font-weight: 400;\">n-1 <\/span><\/i><i><span style=\"font-weight: 400;\">+ F<\/span><\/i><i><span style=\"font-weight: 400;\">n-2<\/span><\/i><i><span style=\"font-weight: 400;\"> for every n&gt;1 <\/span><\/i><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-a-circle\/\">Area of a Circle<\/a><\/strong><\/p>\n<h2><span style=\"font-weight: 400;\">Fibonacci Sequence List <\/span><\/h2>\n<p><span style=\"font-weight: 400;\">As we know the Fibonacci sequence is defined by the below-mentioned formula: <\/span><\/p>\n<p><i><span style=\"font-weight: 400;\">F<\/span><\/i><i><span style=\"font-weight: 400;\">n<\/span><\/i><i><span style=\"font-weight: 400;\"> = F<\/span><\/i><i><span style=\"font-weight: 400;\">n-1 <\/span><\/i><i><span style=\"font-weight: 400;\">+ F<\/span><\/i><i><span style=\"font-weight: 400;\">n-2<\/span><\/i><i><span style=\"font-weight: 400;\"> for every n&gt;1<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, the list of the first 20 terms of the Fibonacci sequence is discussed below:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">0 <\/span><span style=\"font-weight: 400;\">= 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">1 <\/span><span style=\"font-weight: 400;\">= 1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">2 <\/span><span style=\"font-weight: 400;\">= 1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">3 <\/span><span style=\"font-weight: 400;\">= 2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">4 <\/span><span style=\"font-weight: 400;\">= 3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">5 <\/span><span style=\"font-weight: 400;\">= 5<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">6 <\/span><span style=\"font-weight: 400;\">= 8<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">7 <\/span><span style=\"font-weight: 400;\">= 13<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">8 <\/span><span style=\"font-weight: 400;\">= 21<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">9 <\/span><span style=\"font-weight: 400;\">= 34<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">10 <\/span><span style=\"font-weight: 400;\">= 55<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">11 <\/span><span style=\"font-weight: 400;\">= 89<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">12 <\/span><span style=\"font-weight: 400;\">= 144<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">13 <\/span><span style=\"font-weight: 400;\">= 233<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">14 <\/span><span style=\"font-weight: 400;\">= 377<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">15 <\/span><span style=\"font-weight: 400;\">= 610<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">16 <\/span><span style=\"font-weight: 400;\">= 987<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">17 <\/span><span style=\"font-weight: 400;\">= 1597<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">18 <\/span><span style=\"font-weight: 400;\">= 2584<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">19 <\/span><span style=\"font-weight: 400;\">= 4181<\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube\/\">CUBE<\/a><\/strong><\/p>\n<p><span style=\"font-weight: 400;\">This sequence can be seen in the way each term is derived from the sum of the two terms before it, such that:<\/span><\/p>\n<p><i><span style=\"font-weight: 400;\">F<\/span><\/i><i><span style=\"font-weight: 400;\">2<\/span><\/i><i><span style=\"font-weight: 400;\"> = F<\/span><\/i><i><span style=\"font-weight: 400;\">1  <\/span><\/i><i><span style=\"font-weight: 400;\">+ F<\/span><\/i><i><span style=\"font-weight: 400;\">0<\/span><\/i><\/p>\n<p><i><span style=\"font-weight: 400;\">F<\/span><\/i><i><span style=\"font-weight: 400;\">3<\/span><\/i><i><span style=\"font-weight: 400;\"> = F<\/span><\/i><i><span style=\"font-weight: 400;\">2  <\/span><\/i><i><span style=\"font-weight: 400;\">+ F<\/span><\/i><i><span style=\"font-weight: 400;\">1<\/span><\/i><\/p>\n<p><i><span style=\"font-weight: 400;\">F<\/span><\/i><i><span style=\"font-weight: 400;\">4<\/span><\/i><i><span style=\"font-weight: 400;\"> = F<\/span><\/i><i><span style=\"font-weight: 400;\">3  <\/span><\/i><i><span style=\"font-weight: 400;\">+ F<\/span><\/i><i><span style=\"font-weight: 400;\">2<\/span><\/i><\/p>\n<p><i><span style=\"font-weight: 400;\">And so on. <\/span><\/i><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Fibonacci_Sequence_History\"><\/span><span style=\"font-weight: 400;\">Fibonacci Sequence History<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Fibonacci Sequence is named after Leonardo Fibonacci who was an Italian mathematician who introduced this sequence to the Western world in his book Liber Abaci in 1202. The Fibonacci Sequence has earned the nickname &#8220;nature&#8217;s secret code&#8221; due to its remarkable presence in the natural world.<\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/average\/\">Average<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Fibonacci_Sequence_Spiral\"><\/span><span style=\"font-weight: 400;\">Fibonacci Sequence Spiral<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">The Fibonacci spiral is a geometric pattern that emerges from the Fibonacci sequence. It is constructed by drawing a series of connected quarter-circles within a sequence of squares. These squares are sized based on the numbers in the Fibonacci sequence, creating a visually appealing spiral that expands outward infinitely.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"How_to_Draw_a_Fibonacci_Sequence_Spiral\"><\/span><span style=\"font-weight: 400;\">How to Draw a Fibonacci Sequence Spiral<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">To create the Fibonacci spiral, you begin with a small square. <\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Adjacent to it, you draw a larger square whose side length is the sum of the side lengths of the previous two squares. <\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">This process continues, with each new square having a side length equal to the sum of the side lengths of the last two squares. <\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Inside each square, a quarter-circle is drawn, and these quarter-circles connect seamlessly, forming the spiral.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">As the spiral grows, it closely approximates the golden ratio, which is approximately 1.618. The golden ratio is a special number that appears frequently in nature, art, and architecture, known for its special proportions. The Fibonacci spiral, therefore, not only serves as a beautiful mathematical pattern but also highlights the connection between mathematics and the natural world.<\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check:<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/\"> Circumstance of Circle<\/a><\/strong><\/p>\n<h2><span style=\"font-weight: 400;\">Fibonacci Sequence Formula <\/span><\/h2>\n<p><span style=\"font-weight: 400;\">The Fibonacci sequence, denoted as F<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> is defined using a recursive formula, <\/span><\/p>\n<p><i><span style=\"font-weight: 400;\">F<\/span><\/i><i><span style=\"font-weight: 400;\">n<\/span><\/i><i><span style=\"font-weight: 400;\"> = F<\/span><\/i><i><span style=\"font-weight: 400;\">n-1 <\/span><\/i><i><span style=\"font-weight: 400;\">+ F<\/span><\/i><i><span style=\"font-weight: 400;\">n-2<\/span><\/i><i><span style=\"font-weight: 400;\"> for every n&gt;1 <\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">starting with the seed values 0 and 1, such that,  F<\/span><span style=\"font-weight: 400;\">0 <\/span><span style=\"font-weight: 400;\">= 0 and F<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\"> = 1.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sequence is structured in two main parts:<\/span><\/p>\n<p><b>Kick-off Part:<\/b> <span style=\"font-weight: 400;\">This consists of the initial seed values that start the sequence: <\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">0 <\/span><span style=\"font-weight: 400;\">= 0 and F<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\"> = 1<\/span><\/p>\n<p><b>Recursive Relation:<\/b> <span style=\"font-weight: 400;\">This defines how each subsequent term is calculated:<\/span><\/p>\n<p><i><span style=\"font-weight: 400;\">F<\/span><\/i><i><span style=\"font-weight: 400;\">n<\/span><\/i><i><span style=\"font-weight: 400;\"> = F<\/span><\/i><i><span style=\"font-weight: 400;\">n-1 <\/span><\/i><i><span style=\"font-weight: 400;\">+ F<\/span><\/i><i><span style=\"font-weight: 400;\">n-2<\/span><\/i><i><span style=\"font-weight: 400;\"> for every n&gt;1<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">It&#8217;s important to note that the sequence begins with 0, not 1. This means that the position of each term is crucial when discussing the sequence. For example, F<\/span><span style=\"font-weight: 400;\">5<\/span><span style=\"font-weight: 400;\"> is the 6th term in the sequence because the counting starts from F<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">. The sequence up to F<\/span><span style=\"font-weight: 400;\">5<\/span><span style=\"font-weight: 400;\"> looks like this:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><span style=\"font-weight: 400;\">1st term <\/span><\/td>\n<td><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">0 <\/span><span style=\"font-weight: 400;\">= 0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">2nd term <\/span><\/td>\n<td><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">1 <\/span><span style=\"font-weight: 400;\">= 1<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">3rd term <\/span><\/td>\n<td><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">2 <\/span><span style=\"font-weight: 400;\">= 1<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">4th term <\/span><\/td>\n<td><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">3 <\/span><span style=\"font-weight: 400;\">= 2<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">5th term <\/span><\/td>\n<td><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">4 <\/span><span style=\"font-weight: 400;\">= 3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">6th term <\/span><\/td>\n<td><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">5 <\/span><span style=\"font-weight: 400;\">= 5<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-weight: 400;\">Thus, the 6th term in the Fibonacci sequence is equal to 5. This recursive nature and careful indexing are what give the Fibonacci sequence its unique structure and properties, often seen in various natures. <\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/acute-angles\/\">Acute Angle<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Fibonacci_Sequence_Properties\"><\/span><span style=\"font-weight: 400;\">Fibonacci Sequence Properties<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Below discussed are the properties and patterns of the Fibonacci sequence:<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"1_Connection_to_the_Golden_Ratio\"><\/span><span style=\"font-weight: 400;\">1. Connection to the Golden Ratio<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Fibonacci numbers are closely related to the golden ratio, denoted as <\/span><span style=\"font-weight: 400;\"> where <\/span><span style=\"font-weight: 400;\"> = 1.618034. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">The Fibonacci number F<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> can be approximated using the Binet formula:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> &#8211; <\/span><span style=\"font-weight: 400;\">(1 &#8211; <\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\">n<\/span> <span style=\"font-weight: 400;\">5<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example, to find F<\/span><span style=\"font-weight: 400;\">7 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">7  <\/span><span style=\"font-weight: 400;\"> =  <\/span><span style=\"font-weight: 400;\">(1.618034)<\/span><span style=\"font-weight: 400;\">7<\/span><span style=\"font-weight: 400;\"> &#8211; <\/span><span style=\"font-weight: 400;\">(1 &#8211; 1.618034)<\/span><span style=\"font-weight: 400;\">7<\/span> <span style=\"font-weight: 400;\">5<\/span> <span style=\"font-weight: 400;\"> 13<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This shows that as n increases, the Fibonacci number can be accurately predicted using the golden ratio.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_Ratio_of_Successive_Fibonacci_Numbers\"><\/span><span style=\"font-weight: 400;\">2. Ratio of Successive Fibonacci Numbers<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The ratio of successive Fibonacci numbers approaches the golden ratio as the numbers increase:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">n + 1<\/span><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">n<\/span> <span style=\"font-weight: 400;\">1.618034 as n <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Here&#8217;s how the ratio evolves with increasing Fibonacci numbers:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><span style=\"font-weight: 400;\">A<\/span><\/td>\n<td><span style=\"font-weight: 400;\">B<\/span><\/td>\n<td><span style=\"font-weight: 400;\">A\/B<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">3<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1.5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">3<\/span><\/td>\n<td><span style=\"font-weight: 400;\">5<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1.6<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">5<\/span><\/td>\n<td><span style=\"font-weight: 400;\">8<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1.6<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">8<\/span><\/td>\n<td><span style=\"font-weight: 400;\">13<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1.625<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">144<\/span><\/td>\n<td><span style=\"font-weight: 400;\">233<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1.618055555..<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">233<\/span><\/td>\n<td><span style=\"font-weight: 400;\">377<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1.618025751&#8230;<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-weight: 400;\">By multiplying a Fibonacci number by the golden ratio, you get an approximation of the next number in the sequence. For instance:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">13 <\/span><span style=\"font-weight: 400;\"> 1.618034 <\/span><span style=\"font-weight: 400;\"> 21.034442<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This result is close to 21, which is indeed the next Fibonacci number after 13.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_Patterns_in_Multiples\"><\/span><span style=\"font-weight: 400;\">3. Patterns in Multiples<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The Fibonacci sequence also exhibits patterns related to multiples:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Every 3rd number in the sequence (starting from 2) is a multiple of 2.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Every 4th number (starting from 3) is a multiple of 3.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Every 5th number (starting from 5) is a multiple of 5.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">These patterns continue for larger numbers as well, illustrating the sequence&#8217;s inherent mathematical symmetry.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_Fibonacci_Sequence_Below_Zero\"><\/span><span style=\"font-weight: 400;\">4. Fibonacci Sequence Below Zero<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The Fibonacci sequence extends into negative indices using the formula:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">-n <\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">(-1)<\/span><span style=\"font-weight: 400;\">n+1<\/span><span style=\"font-weight: 400;\"> F<\/span><span style=\"font-weight: 400;\">n<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example: <\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">-4<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">(-1)<\/span><span style=\"font-weight: 400;\">5<\/span><span style=\"font-weight: 400;\"> F<\/span><span style=\"font-weight: 400;\">4 <\/span><span style=\"font-weight: 400;\">= -1 <\/span><span style=\"font-weight: 400;\"> 3 = -3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This property shows that the Fibonacci sequence is symmetric around zero, with negative indices producing a mirrored sequence.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_Sum_of_Fibonacci_Numbers\"><\/span><span style=\"font-weight: 400;\">5. Sum of Fibonacci Numbers<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The sum of the first n terms of the Fibonacci sequence can be calculated as:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">i=0<\/span><span style=\"font-weight: 400;\">n<\/span> <span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">i<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">n+2<\/span><span style=\"font-weight: 400;\"> &#8211; 1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example, the sum of the first 10 terms is:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">i=0<\/span><span style=\"font-weight: 400;\">9<\/span> <span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">i<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">F<\/span><span style=\"font-weight: 400;\">12<\/span><span style=\"font-weight: 400;\"> &#8211; 1 = 89 &#8211; 1 = 88<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This formula provides a quick way to sum up the terms of the sequence.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_Connections_to_Other_Mathematical_Concepts\"><\/span><span style=\"font-weight: 400;\">6. Connections to Other Mathematical Concepts<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The Fibonacci sequence also links to other mathematical constructs:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Lucas Numbers: It is similar to Fibonacci numbers but with different starting values.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Pascal&#8217;s Triangle: Fibonacci numbers can be found in the sums of the diagonals of Pascal&#8217;s Triangle.<\/span><\/li>\n<\/ul>\n<h2><span style=\"font-weight: 400;\">Fibonacci Sequence in Real Life <\/span><\/h2>\n<p><span style=\"font-weight: 400;\">One can find the Fibonacci sequence in the spiral arrangements of sunflower seeds. More such examples of the Fibonacci Sequence in Real Life include the petals of daisies and the structure of broccoli and cauliflower. Even the intricate curves of seashells follow this numerical pattern of the Fibonacci Sequence.  <\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Fibonacci Sequence: FAQs <\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_Fibonacci_Sequence\"><\/span>What is the Fibonacci Sequence?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe Fibonacci sequence is a series of numbers where each term is the sum of the two preceding ones. It begins with 0 and 1 and continues infinitely as 0, 1, 1, 2, 3, 5, 8, 13, and so on.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Why_is_the_Fibonacci_Sequence_Significant\"><\/span>Why is the Fibonacci Sequence Significant?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe Fibonacci sequence is significant because the ratio of two successive Fibonacci numbers approximates the golden ratio, which is approximately 1.618034. This ratio appears frequently in nature, art, and architecture, representing a pattern of growth and harmony.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_Are_the_First_10_Fibonacci_Numbers\"><\/span>What Are the First 10 Fibonacci Numbers?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe first 10 numbers in the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_Is_the_Value_of_the_Golden_Ratio\"><\/span>What Is the Value of the Golden Ratio?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe value of the golden ratio is approximately 1.618034.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the Fibonacci Sequence?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The Fibonacci sequence is a series of numbers where each term is the sum of the two preceding ones. It begins with 0 and 1 and continues infinitely as 0, 1, 1, 2, 3, 5, 8, 13, and so on.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Why is the Fibonacci Sequence Significant?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The Fibonacci sequence is significant because the ratio of two successive Fibonacci numbers approximates the golden ratio, which is approximately 1.618034. This ratio appears frequently in nature, art, and architecture, representing a pattern of growth and harmony.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Are the First 10 Fibonacci Numbers?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The first 10 numbers in the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Is the Value of the Golden Ratio?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The value of the golden ratio is approximately 1.618034.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>The Fibonacci Sequence is a series of numbers that begins with 0 and 1. Each number that follows in this [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Fibonacci Sequence","_yoast_wpseo_title":"Fibonacci Sequence - Explanation, Formula, List, Types, & History","_yoast_wpseo_metadesc":"Fibonacci sequence is a sequence of numbers in which each number is sum of the previous two. First two numbers in the sequence are 0 and 1","custom_permalink":"maths\/fibonacci-sequence\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Fibonacci Sequence - Explanation, Formula, List, Types, &amp; History<\/title>\n<meta name=\"description\" content=\"Fibonacci sequence is a sequence of numbers in which each number is sum of the previous two. First two numbers in the sequence are 0 and 1\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fibonacci Sequence - Explanation, Formula, List, Types, &amp; History\" \/>\n<meta property=\"og:description\" content=\"Fibonacci sequence is a sequence of numbers in which each number is sum of the previous two. First two numbers in the sequence are 0 and 1\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-25T19:01:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-08-29T07:10:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"vipin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Fibonacci Sequence - Explanation, Formula, List, Types, & History","description":"Fibonacci sequence is a sequence of numbers in which each number is sum of the previous two. First two numbers in the sequence are 0 and 1","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/","og_locale":"en_US","og_type":"article","og_title":"Fibonacci Sequence - Explanation, Formula, List, Types, & History","og_description":"Fibonacci sequence is a sequence of numbers in which each number is sum of the previous two. First two numbers in the sequence are 0 and 1","og_url":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-03-25T19:01:03+00:00","article_modified_time":"2024-08-29T07:10:27+00:00","og_image":[{"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52.png"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"vipin","Est. reading time":"7 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#primaryimage","inLanguage":"en-US","url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52.png","contentUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52.png","width":1640,"height":924,"caption":"Fibonacci Sequence"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/","name":"Fibonacci Sequence - Explanation, Formula, List, Types, & History","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"primaryImageOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#primaryimage"},"datePublished":"2022-03-25T19:01:03+00:00","dateModified":"2024-08-29T07:10:27+00:00","description":"Fibonacci sequence is a sequence of numbers in which each number is sum of the previous two. First two numbers in the sequence are 0 and 1","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Fibonacci Sequence"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2"},"headline":"Fibonacci Sequence","datePublished":"2022-03-25T19:01:03+00:00","dateModified":"2024-08-29T07:10:27+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#webpage"},"wordCount":1182,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/#primaryimage"},"thumbnailUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/CBSE-52.png","articleSection":["Maths"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2","name":"vipin","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","caption":"vipin"},"sameAs":["http:\/\/surge.infinitylearn.com"],"url":"https:\/\/infinitylearn.com\/surge\/author\/vipin\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/155322"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=155322"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/155322\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=155322"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=155322"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=155322"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=155322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}