{"id":8236,"date":"2021-11-17T16:27:44","date_gmt":"2021-11-17T10:57:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8236"},"modified":"2021-11-17T16:31:17","modified_gmt":"2021-11-17T11:01:17","slug":"if-the-4th-and-9th-terms-of-a-g-p-be-54-and-13122-respectively-find-the-g-p","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-the-4th-and-9th-terms-of-a-g-p-be-54-and-13122-respectively-find-the-g-p\/","title":{"rendered":"If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, find the G.P."},"content":{"rendered":"

Solution :<\/h2>\n

Let a be the first term and r the common ratio of the given G.P. Then,<\/p>\n

\\(a_4\\) = 54\u00a0 and\u00a0 \\(a_9\\) = 13122<\/p>\n

\\(\\implies\\)\u00a0 \\(ar^3\\) = 54\u00a0 \u00a0and\u00a0 \\(ar^8\\)\u00a0 =\u00a0 13122<\/p>\n

\\(\\implies\\)\u00a0 \\(ar^8\\over ar^3\\) = \\(13122\\over 54\\)\u00a0 \\(\\implies\\)\u00a0 \\(r^5\\) = 245\u00a0 \\(\\implies\\)\u00a0 r = 3<\/p>\n

Putting r = 3 in \\(ar^3\\) = 54,<\/p>\n

we get a = 2.<\/p>\n

Hence, the given G.P is 2, 6, 18, 54, ….<\/p>\n

\n

Similar Questions<\/h3>\n

Three positive integers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then the common ratio of GP is<\/a><\/p>\n

A man saves Rs 200 in each of the first three months of his service. In each of the subsequent months, his saving increases by Rs 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs 11040 after<\/a><\/p>\n

If 100 times the 100th term of an AP with non-zero common difference equal to the 50 times its 50th term, then the 150th term of AP is<\/a><\/p>\n

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, \u2026\u2026. , is<\/a><\/p>\n

Find the sum of n terms of the series 1.3.5 + 3.5.7 + 5.7.9 + \u2026\u2026<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let a be the first term and r the common ratio of the given G.P. Then, \\(a_4\\) = 54\u00a0 and\u00a0 \\(a_9\\) = 13122 \\(\\implies\\)\u00a0 \\(ar^3\\) = 54\u00a0 \u00a0and\u00a0 \\(ar^8\\)\u00a0 =\u00a0 13122 \\(\\implies\\)\u00a0 \\(ar^8\\over ar^3\\) = \\(13122\\over 54\\)\u00a0 \\(\\implies\\)\u00a0 \\(r^5\\) = 245\u00a0 \\(\\implies\\)\u00a0 r = 3 Putting r = 3 in \\(ar^3\\) = 54, …<\/p>\n

If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, find the G.P.<\/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":[43,57],"tags":[],"yoast_head":"\nIf the 4th and 9th terms of a G.P. be 54 and 13122 respectively, find the G.P.<\/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\/if-the-4th-and-9th-terms-of-a-g-p-be-54-and-13122-respectively-find-the-g-p\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, find the G.P.\" \/>\n<meta property=\"og:description\" content=\"Solution : Let a be the first term and r the common ratio of the given G.P. Then, (a_4) = 54\u00a0 and\u00a0 (a_9) = 13122 (implies)\u00a0 (ar^3) = 54\u00a0 \u00a0and\u00a0 (ar^8)\u00a0 =\u00a0 13122 (implies)\u00a0 (ar^8over ar^3) = (13122over 54)\u00a0 (implies)\u00a0 (r^5) = 245\u00a0 (implies)\u00a0 r = 3 Putting r = 3 in (ar^3) = 54, … If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, find the G.P. 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Then, (a_4) = 54\u00a0 and\u00a0 (a_9) = 13122 (implies)\u00a0 (ar^3) = 54\u00a0 \u00a0and\u00a0 (ar^8)\u00a0 =\u00a0 13122 (implies)\u00a0 (ar^8over ar^3) = (13122over 54)\u00a0 (implies)\u00a0 (r^5) = 245\u00a0 (implies)\u00a0 r = 3 Putting r = 3 in (ar^3) = 54, … If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, find the G.P. 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