{"id":8270,"date":"2021-11-20T01:09:24","date_gmt":"2021-11-19T19:39:24","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8270"},"modified":"2021-11-20T01:30:38","modified_gmt":"2021-11-19T20:00:38","slug":"find-the-9th-term-in-the-expansion-of-xover-a-3aover-x212","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-9th-term-in-the-expansion-of-xover-a-3aover-x212\/","title":{"rendered":"Find the 9th term in the expansion of \\(({x\\over a} – {3a\\over x^2})^{12}\\)."},"content":{"rendered":"

Solution :<\/h2>\n

We know that the (r + 1)th term or general term in the expansion<\/a> of \\((x + a)^n\\) is given by<\/p>\n

\\(T_{r + 1}\\) = \\(^{n}C_r x^{n – r} a^r\\)<\/p>\n

In the expansion of \\(({x\\over a} – {3a\\over x^2})^{12}\\), we have<\/p>\n

\\(T_{9}\\) = \\(T_{8 + 1}\\) = \\(^{12}C_8 ({x\\over a})^{12 – 8} ({-3a\\over x^2})^8\\)<\/p>\n

\\(\\implies\\) \\(T_{9}\\) = \\(^{12}C_8 ({x\\over a})^4 ({-3a\\over x^2})^8\\)<\/p>\n

\\(\\implies\\) \\(T_{9}\\) = \\(^{12}C_4\\) \\(3^8 a^4\\over x^{12}\\) = \\((^{12}C_4 x^{-12} a^4)3^8\\)<\/p>\n

\n

Similar Questions<\/h3>\n

Find the middle term in the expansion of \\(({2\\over 3}x^2 \u2013 {3\\over 2x})^{20}\\).<\/a><\/p>\n

Find the middle term in the expansion of \\((3x \u2013 {x^3\\over 6})^7\\).<\/a><\/p>\n

Find the 10th term in the binomial expansion of \\((2x^2 + {1\\over x})^{12}\\).<\/a><\/p>\n

Which is larger \\((1.01)^{1000000}\\) or 10,000?<\/a><\/p>\n

By using binomial theorem, expand \\((1 + x + x^2)^3\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We know that the (r + 1)th term or general term in the expansion of \\((x + a)^n\\) is given by \\(T_{r + 1}\\) = \\(^{n}C_r x^{n – r} a^r\\) In the expansion of \\(({x\\over a} – {3a\\over x^2})^{12}\\), we have \\(T_{9}\\) = \\(T_{8 + 1}\\) = \\(^{12}C_8 ({x\\over a})^{12 – 8} ({-3a\\over …<\/p>\n

Find the 9th term in the expansion of \\(({x\\over a} – {3a\\over x^2})^{12}\\).<\/span> Read More »<\/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":"\nFind the 9th term in the expansion of \\(({x\\over a} - {3a\\over x^2})^{12}\\).<\/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-9th-term-in-the-expansion-of-xover-a-3aover-x212\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the 9th term in the expansion of \\(({x\\over a} - {3a\\over x^2})^{12}\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : We know that the (r + 1)th term or general term in the expansion of ((x + a)^n) is given by (T_{r + 1}) = (^{n}C_r x^{n – r} a^r) In the expansion of (({xover a} – {3aover x^2})^{12}), we have (T_{9}) = (T_{8 + 1}) = (^{12}C_8 ({xover a})^{12 – 8} ({-3aover … Find the 9th term in the expansion of (({xover a} – {3aover x^2})^{12}). 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