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CTK Exchange
ke_45

guest
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Jun-17-08, 10:59 AM (EST) |
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"Geometric series ratios"
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We have an arithmetic progression the squares of whose 12h, 13th, and 15th terms form a geometric progression. Find all the ratios of this progression. Assuming u_n+1 = u_n + d -or- u_n+1 = u_1 + d*n for the arithmetic progression, and u_n+1 = u_n * q -or- u_n+1 = u_1 * q^(n-1) for the geometric one, how do we go about this? (My results don't match with the answer in the book I took this from.) Please only hint, don't solve! Thanks -- KE
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alexb
Charter Member
2236 posts |
Jun-17-08, 11:02 AM (EST) |
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1. "RE: Geometric series ratios"
In response to message #0
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If the initial arithmetic progrssion is a +i·d, then the condition is (a + 15d)² / (a + 13d)² = (a + 13d)² / (a + 12d)² which gives you (a + 15d)² · (a + 11d)² = (a + 13d)² · (a + 13d)². There are two ways to get rid of the square. Try both. |
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