{"id":665401,"date":"2023-07-24T15:27:31","date_gmt":"2023-07-24T09:57:31","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=665401"},"modified":"2025-07-25T17:28:40","modified_gmt":"2025-07-25T11:58:40","slug":"geometric-progression-and-sum-of-gp-formula-limitations-example","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/","title":{"rendered":"Geometric Progression and Sum of GP &#8211; Formula Limitations &#038; Example"},"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\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#Introduction_to_Sum_of_terms_of_Geometric_Progression\" title=\"Introduction to Sum of terms of Geometric Progression\">Introduction to Sum of terms of Geometric Progression<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#What_is_sum_of_GP\" title=\"What is sum of GP\">What is sum of GP<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#Formula_for_infinite_GP\" title=\"Formula for infinite GP\">Formula for infinite GP<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#Limitations_and_convergence_of_sum_of_GP\" title=\"Limitations and convergence of sum of GP\">Limitations and convergence of sum of GP<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#Conclusion\" title=\"Conclusion\">Conclusion<\/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\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#Frequently_asked_questions_Sum_of_GP\" title=\"Frequently asked questions Sum of GP\">Frequently asked questions Sum of GP<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#What_is_the_geometric_progression_first_n_terms_total_value\" title=\"What is the geometric progression first n terms total value? \">What is the geometric progression first n terms total value? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#A_geometric_path_that_is_infinitely_long_can_either_converge_or_diverge_so_how_can_we_tell\" title=\"A geometric path that is infinitely long can either converge or diverge, so how can we tell? \">A geometric path that is infinitely long can either converge or diverge, so how can we tell? <\/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\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#When_a_geometric_progression_is_endless_may_its_sum_be_negative\" title=\"When a geometric progression is endless, may its sum be negative? \">When a geometric progression is endless, may its sum be negative? <\/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\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#What_occurs_if_a_geometric_progressions_common_ratio_is_equal_to_1\" title=\"What occurs if a geometric progression&#039;s common ratio is equal to 1? \">What occurs if a geometric progression&#039;s common ratio is equal to 1? <\/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\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#What_is_the_sum_of_geometric_progression_formula_for_infinite_terms\" title=\"What is the sum of geometric progression formula for infinite terms \">What is the sum of geometric progression formula for infinite terms <\/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\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#What_is_the_sum_of_n_terms_of_geometric_progression_when_r_1\" title=\"What is the sum of n terms of geometric progression when r =1.\">What is the sum of n terms of geometric progression when r =1.<\/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\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#When_does_the_sum_of_infinite_GP_converge\" title=\"When does the sum of infinite GP converge: \">When does the sum of infinite GP converge: <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#What_is_the_sum_of_first_n_terms_in_Geometric_Sequence\" title=\"What is the sum of first n terms in Geometric Sequence \">What is the sum of first n terms in Geometric Sequence <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/#What_is_the_sum_of_the_infinite_GP_when_the_common_ratio_is\" title=\"What is the sum of the infinite GP when the common ratio is \">What is the sum of the infinite GP when the common ratio is <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Sum_of_terms_of_Geometric_Progression\"><\/span>Introduction to Sum of terms of Geometric Progression<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A geometric progression (also known as a geometric sequence) is a numerical series in which each term is created by multiplying the preceding term by a constant factor known as the common ratio. The sum of terms in a geometric progression is a fundamental notion that allows us to compute the total value produced by adding all of the elements in the sequence. This article investigates the formula for calculating the sum of terms, its restrictions, convergence, and examples, as well as commonly asked issues and solutions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_is_sum_of_GP\"><\/span>What is sum of GP<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The formula for calculating the sum of terms in a finite or infinite geometric progression is different.<\/p>\n<ul>\n<li>Formula for sum of n terms of GP<\/li>\n<\/ul>\n<p>Sum of a Finite Geometric Progression: The sum (denoted by &#8220;S&#8221;) of a geometric progression with &#8220;n&#8221; terms may be determined using the formula:<\/p>\n<p><strong>S = a(r<sup>n<\/sup> &#8211; 1)\/r &#8211; 1<\/strong><\/p>\n<p>In this case, &#8220;<em><span style=\"text-decoration: underline;\">a<\/span><\/em>&#8221; stands for the first term, &#8220;<em>r<\/em>&#8221; stands for the common ratio, and <em>&#8220;n&#8221;<\/em> stands for the number of terms.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Formula_for_infinite_GP\"><\/span>Formula for infinite GP<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>Sum of an Infinite Geometric Progression: The sum (denoted by &#8220;S&#8221;) of an infinite geometric progression (where the common ratio &#8220;r&#8221; is between -1 and 1) can be computed using the formula:<\/li>\n<li><strong>S = a\/1 &#8211; r.<\/strong> The collection of input values for which the function is defined is referred to as the domain.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Limitations_and_convergence_of_sum_of_GP\"><\/span>Limitations and convergence of sum of GP<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>Limitations: The sum of a finite geometric progression formula is only valid when the number of terms is known.<\/li>\n<li>Only when the common ratio is between -1 and 1 can the formula for the sum of an infinite geometric progression be used.<\/li>\n<li>An infinite geometric progression converges if the common ratio&#8217;s absolute value is less than one (|r| 1).<\/li>\n<li>An infinite geometric progression&#8217;s total converges to a finite value when |r| 1.<\/li>\n<li>If |r| is less than 1, the total approaches infinity or oscillates without a fixed value, which is known as the infinite geometric progression diverging.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Conclusion\"><\/span>Conclusion<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The sum of terms in a geometric progression is important in many mathematical applications, such as physics, engineering, and finance. We can compute the sum of terms precisely and interpret the results by comprehending the formulas, restrictions, and convergence features. The formula offers a potent tool to assess the cumulative value generated by adding the terms in the sequence, regardless of whether it is a finite or infinite geometric progression.<\/p>\n<p>Problems related sum of GP<\/p>\n<ul>\n<li>Finite geometric progression illustration<\/li>\n<li>Consider the geometric progression where the initial term (a), common ratio (r), and number of terms (n) are all equal to 2, 3, and 4. Using the following formula to calculate the total of a finite geometric progression:<br \/>\nS = 2 * (3^4 &#8211; 1) \/ (3 &#8211; 1)<br \/>\nS = 2 * (81 &#8211; 1) \/ 2 S = 80<\/li>\n<\/ul>\n<ul>\n<li>Infinite geometric progression illustration Think about the geometric progression where the common ratio (r) is 1\/2 and the first term (a) is 1. Solution: Using the sum of an infinite geometric progression formula:<br \/>\nS = 1 \/ (1 &#8211; 1\/2)<br \/>\nS= 1 \/ (1\/2)<br \/>\nS = 2<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_asked_questions_Sum_of_GP\"><\/span>Frequently asked questions Sum of GP<span class=\"ez-toc-section-end\"><\/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_geometric_progression_first_n_terms_total_value\"><\/span>What is the geometric progression first n terms total value? <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 formula S = a * (1 - rn) \/ (1 - r) can be used to compute the sum of the first 'n' terms.\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=\"A_geometric_path_that_is_infinitely_long_can_either_converge_or_diverge_so_how_can_we_tell\"><\/span>A geometric path that is infinitely long can either converge or diverge, so how can we tell? <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\tIf the common ratio (|r|) has an absolute value smaller than 1, an infinite geometric progression converges. Otherwise, it turns off. \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=\"When_a_geometric_progression_is_endless_may_its_sum_be_negative\"><\/span>When a geometric progression is endless, may its sum be negative? <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\tIf the common ratio is negative and the terms in the series alternate signs, the sum can indeed be negative. \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_occurs_if_a_geometric_progressions_common_ratio_is_equal_to_1\"><\/span>What occurs if a geometric progression&#039;s common ratio is equal to 1? <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\t All terms in the sequence will be identical if the common ratio is 1, and the sum will be the product of the common ratio and the number of terms.\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_sum_of_geometric_progression_formula_for_infinite_terms\"><\/span>What is the sum of geometric progression formula for infinite terms <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\tS = a \/ (1 - r), where 'a' denotes the sequence's initial term and 'r' denotes its common ratio, is the formula for an infinite geometric progression's sum. With the help of an infinite number of terms in the sequence, this formula calculates the total value.\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_sum_of_n_terms_of_geometric_progression_when_r_1\"><\/span>What is the sum of n terms of geometric progression when r =1.<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 formula S = n * a, where 'n' is the number of terms and 'a' is the first term, can be used to calculate the sum of 'n' terms in a geometric progression when the common ratio (r) is equal to 1. The sum in this instance is only the first term multiplied by the number of terms. \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=\"When_does_the_sum_of_infinite_GP_converge\"><\/span>When does the sum of infinite GP converge: <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\tWhen the common ratio (|r|) is smaller than 1, the sum of an infinite geometric progression converges. In these scenarios, the sum gets closer to a limited value. If the common ratio's absolute value is larger than or equal to 1, the series diverges and does not have a finite total. \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_sum_of_first_n_terms_in_Geometric_Sequence\"><\/span>What is the sum of first n terms in Geometric 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 formula for calculating the sum of the first 'n' terms in a geometric sequence is S = a * (1 - rn) \/ (1 - r), where 'a' stands for the first term and 'r' is the common ratio. The cumulative value obtained by adding the stated number of terms in the sequence is calculated using this equation.\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_sum_of_the_infinite_GP_when_the_common_ratio_is\"><\/span>What is the sum of the infinite GP when the common ratio is <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 total of the infinite series depends on the value of the first term (a) when the common ratio (r) in a geometric progression equals 1. The series diverges and does not have a finite sum if an is less than 0. The sum of all terms is 0 if a = 0.\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 geometric progression first n terms total value? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula S = a * (1 - rn) \/ (1 - r) can be used to compute the sum of the first 'n' terms.\"\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\": \"A geometric path that is infinitely long can either converge or diverge, so how can we tell? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"If the common ratio (|r|) has an absolute value smaller than 1, an infinite geometric progression converges. Otherwise, it turns off.\"\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\": \"When a geometric progression is endless, may its sum be negative? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"If the common ratio is negative and the terms in the series alternate signs, the sum can indeed be negative.\"\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 occurs if a geometric progression's common ratio is equal to 1? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"All terms in the sequence will be identical if the common ratio is 1, and the sum will be the product of the common ratio and the number of terms.\"\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 sum of geometric progression formula for infinite terms \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"S = a \/ (1 - r), where 'a' denotes the sequence's initial term and 'r' denotes its common ratio, is the formula for an infinite geometric progression's sum. With the help of an infinite number of terms in the sequence, this formula calculates the total value.\"\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 sum of n terms of geometric progression when r =1.\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula S = n * a, where 'n' is the number of terms and 'a' is the first term, can be used to calculate the sum of 'n' terms in a geometric progression when the common ratio (r) is equal to 1. The sum in this instance is only the first term multiplied by the number of terms.\"\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\": \"When does the sum of infinite GP converge: \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"When the common ratio (|r|) is smaller than 1, the sum of an infinite geometric progression converges. In these scenarios, the sum gets closer to a limited value. If the common ratio's absolute value is larger than or equal to 1, the series diverges and does not have a finite total.\"\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 sum of first n terms in Geometric Sequence \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula for calculating the sum of the first 'n' terms in a geometric sequence is S = a * (1 - rn) \/ (1 - r), where 'a' stands for the first term and 'r' is the common ratio. The cumulative value obtained by adding the stated number of terms in the sequence is calculated using this equation.\"\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 sum of the infinite GP when the common ratio is \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The total of the infinite series depends on the value of the first term (a) when the common ratio (r) in a geometric progression equals 1. The series diverges and does not have a finite sum if an is less than 0. The sum of all terms is 0 if a = 0.\"\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>Introduction to Sum of terms of Geometric Progression A geometric progression (also known as a geometric sequence) is a numerical [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Sum of GP","_yoast_wpseo_title":"Geometric Progression and Sum of GP - Formula Limitations & Example","_yoast_wpseo_metadesc":"The \"Sum of GP\" refers to the total result obtained by adding all the terms of a Geometric Progression sequence together.","custom_permalink":"articles\/geometric-progression-and-sum-of-gp-formula-limitations-example\/"},"categories":[8442,8443],"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>Geometric Progression and Sum of GP - 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