{"id":156370,"date":"2022-03-26T01:40:54","date_gmt":"2022-03-25T20:10:54","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/sequence-and-series\/"},"modified":"2022-12-22T21:38:33","modified_gmt":"2022-12-22T16:08:33","slug":"sequence-and-series","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/sequence-and-series\/","title":{"rendered":"Sequence and Series"},"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\/sequence-and-series\/#Definition_of_Sequence_and_Series\" title=\"Definition of Sequence and Series\">Definition of Sequence and Series<\/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\/sequence-and-series\/#Types_of_Sequences\" title=\"Types of Sequences\">Types of Sequences<\/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\/sequence-and-series\/#Difference_Between_Sequence_and_Series\" title=\"Difference Between Sequence and Series\">Difference Between Sequence and Series<\/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\/sequence-and-series\/#Sequence_and_Series_Formulas\" title=\"Sequence and Series Formulas\">Sequence and Series Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/sequence-and-series\/#Formula_for_Series\" title=\"Formula for Series\">Formula for Series<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Definition_of_Sequence_and_Series\"><\/span>Definition of Sequence and Series<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Sequence<br \/>\nA sequence is a set of numbers that are placed in order.<\/p>\n<p>Series<br \/>\nA series is a set of numbers that are placed in order and have a sum.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156369 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/sequence-and-series.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/sequence-and-series.jpg?v=1648239051 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/sequence-and-series-300x212.jpg?v=1648239051 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Sequences\"><\/span>Types of Sequences<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are many types of sequences, but some of the more common ones are arithmetic, geometric, and harmonic.<\/p>\n<p>An arithmetic sequence is a sequence of numbers in which each number is the sum of the previous two numbers in the sequence. For example, the sequence 1, 2, 3, 4, 5, would be an arithmetic sequence.<\/p>\n<p>A geometric sequence is a sequence of numbers in which each number is the product of the previous two numbers in the sequence. For example, the sequence 1, 2, 4, 8, 16, would be a geometric sequence.<\/p>\n<p>A harmonic sequence is a sequence of numbers in which each number is the reciprocal of the previous number in the sequence. For example, the sequence 1, 1\/2, 1\/3, 1\/4, 1\/5, would be a harmonic sequence.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Difference_Between_Sequence_and_Series\"><\/span>Difference Between Sequence and Series<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-size: 14pt;\"><strong>Sequence:<\/strong><\/span><\/p>\n<p>A sequence is a set of numbers that are placed in a certain order. The numbers in a sequence can be any type of number, including real numbers, integers, or rational numbers. There are a few different types of sequences, but the most common type is a arithmetic sequence.<\/p>\n<p><span style=\"font-size: 14pt;\"><strong>Series:<\/strong><\/span><\/p>\n<p>A series is a set of numbers that are placed in a certain order and added together. The numbers in a series can be any type of number, including real numbers, integers, or rational numbers. There are a few different types of series, but the most common type is a arithmetic series.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Sequence_and_Series_Formulas\"><\/span>Sequence and Series Formulas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Sequences are a series of numbers that are in a certain order.<\/p>\n<p>The first sequence is 1, 2, 3, 4, 5, 6, 7, 8.<\/p>\n<p>The second sequence is 1, 3, 5, 7, 9, 11, 13.<\/p>\n<p>The third sequence is 2, 4, 6, 8, 10, 12.<\/p>\n<p>The fourth sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.<\/p>\n<p>Sequences can be created by adding or multiplying the previous number in the sequence by a certain number.<\/p>\n<p>The sequence 1, 2, 3, 4, 5, 6, 7, 8 can be created by adding 1 to the previous number.<\/p>\n<p>The sequence 1, 3, 5, 7, 9, 11, 13 can be created by multiplying the previous number by 2.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Formula_for_Series\"><\/span>Formula for Series<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The sum of a series can be found by using the following formula:<\/p>\n<p>S = a + (a + d) + (a + 2d) + (a + 3d) &#8230;..+(a+xd)<\/p>\n<p>where a is the first term in the series, d is the common difference, and S is the sum of the series.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definition of Sequence and Series Sequence A sequence is a set of numbers that are placed in order. Series A [&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":"Sequence and Series","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn Sequence and Series topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts","custom_permalink":"maths\/sequence-and-series\/"},"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>Sequence and Series - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn Sequence and Series topic of Maths in details explained by subject experts on infinitylearn.com. 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