{"id":8273,"date":"2021-11-20T01:15:44","date_gmt":"2021-11-19T19:45:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8273"},"modified":"2021-11-20T01:28:20","modified_gmt":"2021-11-19T19:58:20","slug":"find-the-middle-term-in-the-expansion-of-2over-3x2-3over-2x20","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-middle-term-in-the-expansion-of-2over-3x2-3over-2x20\/","title":{"rendered":"Find the middle term in the expansion of \\(({2\\over 3}x^2 &#8211; {3\\over 2x})^{20}\\)."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Here, n = 20, which is an even number.<\/p>\n<p>So, \\({20\\over 2} + 1\\)th term i.e. 11th term is the <a href=\"https:\/\/mathemerize.com\/middle-term-in-binomial-expansion\/\">middle term<\/a>.<\/p>\n<p>Hence, the <a href=\"https:\/\/mathemerize.com\/middle-term-in-binomial-expansion\/\">middle term<\/a> = \\(T_{11}\\)<\/p>\n<p>\\(T_{11}\\) = \\(T_{10 + 1}\\) = \\(^{20}C_{10}\\) \\(({2\\over 3}x^2)^{20 &#8211; 10}\\) \\((-{3\\over 2x})^{10}\\)<\/p>\n<p>= \\(^{20}C_{10} x^{10}\\)<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-middle-term-in-the-expansion-of-3x-x3over-67\/\" aria-label=\"\u201cFind the middle term in the expansion of \\((3x \u2013 {x^3\\over 6})^7\\).\u201d (Edit)\">Find the middle term in the expansion of \\((3x \u2013 {x^3\\over 6})^7\\).<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-9th-term-in-the-expansion-of-xover-a-3aover-x212\/\" aria-label=\"\u201cFind the 9th term in the expansion of \\(({x\\over a} \u2013 {3a\\over x^2})^{12}\\).\u201d (Edit)\">Find the 9th term in the expansion of \\(({x\\over a} \u2013 {3a\\over x^2})^{12}\\).<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-10th-term-in-the-binomial-expansion-of-2x2-1over-x12\/\" aria-label=\"\u201cFind the 10th term in the binomial expansion of \\((2x^2 + {1\\over x})^{12}\\).\u201d (Edit)\">Find the 10th term in the binomial expansion of \\((2x^2 + {1\\over x})^{12}\\).<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/which-is-larger-1-011000000-or-10000\/\" aria-label=\"\u201cWhich is larger \\((1.01)^{1000000}\\) or 10,000?\u201d (Edit)\">Which is larger \\((1.01)^{1000000}\\) or 10,000?<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/by-using-binomial-theorem-expand-1-x-x23\/\" aria-label=\"\u201cBy using binomial theorem, expand \\((1 + x + x^2)^3\\).\u201d (Edit)\">By using binomial theorem, expand \\((1 + x + x^2)^3\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Here, n = 20, which is an even number. So, \\({20\\over 2} + 1\\)th term i.e. 11th term is the middle term. Hence, the middle term = \\(T_{11}\\) \\(T_{11}\\) = \\(T_{10 + 1}\\) = \\(^{20}C_{10}\\) \\(({2\\over 3}x^2)^{20 &#8211; 10}\\) \\((-{3\\over 2x})^{10}\\) = \\(^{20}C_{10} x^{10}\\) Similar Questions Find the middle term in the expansion &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/find-the-middle-term-in-the-expansion-of-2over-3x2-3over-2x20\/\"> <span class=\"screen-reader-text\">Find the middle term in the expansion of \\(({2\\over 3}x^2 &#8211; {3\\over 2x})^{20}\\).<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[177,43],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Find the middle term in the expansion of \\(({2\\over 3}x^2 - {3\\over 2x})^{20}\\).<\/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:\/\/mathemerize.com\/find-the-middle-term-in-the-expansion-of-2over-3x2-3over-2x20\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the middle term in the expansion of \\(({2\\over 3}x^2 - {3\\over 2x})^{20}\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : Here, n = 20, which is an even number. So, ({20over 2} + 1)th term i.e. 11th term is the middle term. Hence, the middle term = (T_{11}) (T_{11}) = (T_{10 + 1}) = (^{20}C_{10}) (({2over 3}x^2)^{20 &#8211; 10}) ((-{3over 2x})^{10}) = (^{20}C_{10} x^{10}) Similar Questions Find the middle term in the expansion &hellip; Find the middle term in the expansion of (({2over 3}x^2 &#8211; {3over 2x})^{20}). 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So, ({20over 2} + 1)th term i.e. 11th term is the middle term. Hence, the middle term = (T_{11}) (T_{11}) = (T_{10 + 1}) = (^{20}C_{10}) (({2over 3}x^2)^{20 &#8211; 10}) ((-{3over 2x})^{10}) = (^{20}C_{10} x^{10}) Similar Questions Find the middle term in the expansion &hellip; Find the middle term in the expansion of (({2over 3}x^2 &#8211; {3over 2x})^{20}). 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