{"id":16125,"date":"2021-08-12T09:36:58","date_gmt":"2021-08-12T04:06:58","guid":{"rendered":"https:\/\/python-programs.com\/?p=16125"},"modified":"2021-11-22T18:38:26","modified_gmt":"2021-11-22T13:08:26","slug":"python-program-to-find-sum-of-geometric-progression-series","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-find-sum-of-geometric-progression-series\/","title":{"rendered":"Python Program to Find Sum of Geometric Progression Series"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-to-repeat-string-n-times-with-separator\/\">Python Program to Repeat String N times with Separator<\/a><br \/>\n<strong>Geometric progression series<\/strong><\/p>\n<p>A geometric progression series is one in which any two consecutive terms have the same ratio. As a result, we can find the subsequent term by multiplying the common ratio by the previous term.<\/p>\n<p>This is how the series looks:\u00a0 \u00a0<b>a, ar, ar<sup>2<\/sup>, ar<sup>3<\/sup>, ar<sup>4<\/sup>, . . . . .<\/b><\/p>\n<p>where common ratio(r)=2nd term\/1st term (T2\/T1) or (T3\/T2)<\/p>\n<p>Standard Formula to find the sum of series in G.P = \u00a0<strong>a(1 \u2013 r<sup>n<\/sup>)\/(1 \u2013 r)<\/strong><\/p>\n<p>Given First term(a), common ratio(r), Nth term(total number of terms ) in Series, The task is to find Sum of the Geometric Progression Series.<\/p>\n<p>Example: 2,6,18,54,162,486,1458,. . . . . . . .<\/p>\n<p>Here a=2 , r=6\/2 =3 , let n=10<\/p>\n<p>Formula to find Nth term =<b>\u00a0ar<sup>n<\/sup><sup>&#8211;<\/sup><sup>1\u00a0\u00a0<\/sup><\/b><\/p>\n<p>= 39366<\/p>\n<p>sum of series = <strong>a(1 \u2013 r<sup>n<\/sup>)\/(1 \u2013 r) <\/strong>=59048<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given Total number of terms=4\r\nGiven First Term = 3\r\nGiven common ratio = 3<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>The sum of the given geometric progression series = 120<\/pre>\n<p><strong>Example 2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given Total number of terms=6\r\nGiven First Term = 4 \r\nGiven common ratio = 5<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The sum of the given geometric progression series = 15624<\/pre>\n<h2>Program to Find Sum of Geometric Progression Series<\/h2>\n<p>Below are the ways to find the Sum of the Geometric Progression Series.<\/p>\n<ul>\n<li><a href=\"#Using_Mathematical_Formula_(Static_Input)\">Using Mathematical Formula (Static Input)<\/a><\/li>\n<li><a href=\"#Using_Mathematical_Formula_(User_Input)\">Using Mathematical Formula (User Input)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_Mathematical_Formula_(Static_Input)\">Method #1: Using Mathematical Formula (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Import math module using the import keyword.<\/li>\n<li>Give the Total number of terms as static input and store it in a variable.<\/li>\n<li>Give the first term as static input and store it in another variable.<\/li>\n<li>Give the Common Ratio as static input and store it in another variable.<\/li>\n<li>Calculate the given Sum of Geometric Progression Series by using the standard mathematical formula <strong>a(1 \u2013 r<sup>n<\/sup>)\/(1 \u2013 r)<\/strong> and store it in a variable.<\/li>\n<li>Print the sum of the Geometric Progression series.<\/li>\n<li>The Exit of the program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Import math module using import keyword.\r\nimport math\r\n# Give the Total number of terms as static input and store it in a variable.\r\ntot_trms = 10\r\n# Give the first term as static input and store it in a variable.\r\nfst_trm = 2\r\n# Give the Common Ratio as static input and store it in a variable.\r\ncommn_diff = 3\r\n# Calculate the given Sum of Geometric Progression Series by using standard mathematical formula\r\n# a(1 \u2013 r**n)\/(1 \u2013 r) and store it in a variable.\r\nsum_geoprog = (fst_trm*(1-(commn_diff)**tot_trms))\/\/(1-commn_diff)\r\n# Print the sum of Geometric Progression series .\r\nprint(\"The sum of the given geometric progression series = \", sum_geoprog)\r\n<\/pre>\n<p>&nbsp;<\/p>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The sum of the given geometric progression series =  59048<\/pre>\n<h3 id=\"Using_Mathematical_Formula_(User_Input)\">Method #2: Using Mathematical Formula (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Import math module using the import keyword.<\/li>\n<li>Give the Total number of terms as User input using the int(input()) function and store it in a variable.<\/li>\n<li>Give the first term as User input using the int(input()) function and store it in another variable.<\/li>\n<li>Give the Common Ratio as User input using the int(input()) function and store it in another variable.<\/li>\n<li>Calculate the Sum of Geometric Progression Series by using the standard mathematical formula <strong>a(1 \u2013 r<sup>n<\/sup>)\/(1 \u2013 r)<\/strong> and store it in a variable.<\/li>\n<li>Print the sum of the Geometric Progression series.<\/li>\n<li>The Exit of the program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">#Import math module using the import keyword.\r\nimport math\r\n#Give the Total number of terms as User input using\u00a0the\u00a0int(input())\u00a0function\u00a0and store it in a variable.\r\ntot_trms = int(input(\"Given Total number of terms =\"))\r\n#Give the first term as User input using the int(input()) function and store it in another variable.\r\nfst_trm = int(input(\"Given First Term = \"))\r\n#Give the Common Ratio as User input using\u00a0the\u00a0int(input())\u00a0function\u00a0 and store it in another variable.\r\ncommn_diff = int(input(\"Given common ratio = \"))\r\n#Calculate the Sum of Geometric Progression Series by using standard mathematical formula \r\n#a(1 \u2013 r**n)\/(1 \u2013 r) and store it in a variable.\r\nsum_geoprog = (fst_trm*(1-(commn_diff)**tot_trms))\/\/(1-commn_diff)\r\n#Print the sum of Geometric Progression series .\r\nprint(\"The sum of the given geometric progression series = \", sum_geoprog)\r\n\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Given Total number of terms =6\r\nGiven First Term = 4\r\nGiven common ratio = 5\r\nThe sum of the given geometric progression series = 15624<\/pre>\n<p>Explore more instances related to python concepts from\u00a0<a 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Geometric progression series A geometric progression series is one in which any two consecutive terms have the same ratio. As a result, we can find the subsequent term by multiplying the common ratio by the previous term. This is &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-geometric-progression-series\/\"> <span class=\"screen-reader-text\">Python Program to Find Sum of Geometric Progression Series<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":16809,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python Program to Find Sum of Geometric Progression Series - Python Programs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-geometric-progression-series\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program to Find Sum of Geometric Progression Series - Python Programs\" \/>\n<meta property=\"og:description\" content=\"In the previous article, we have discussed Python Program to Repeat String N times with Separator Geometric progression series A geometric progression series is one in which any two consecutive terms have the same ratio. 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