If the 2 n d , 5 t h and 9 t h terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is

Question

If the 2 n d , 5 t h and 9 t h terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is, 1, 7 4, 8 5, 4 3

MARKS App · Accepted Answer

Let the A.P. be a , a + d , a + 2 d , . . . . . Given, a + d . a + 8 d = a + 4 d 2 a 2 + 9 a d + 8 d 2 = a 2 + 8 a d + 16 d 2 8 d 2 - a d = 0 d 8 d - a = 0 ∵ d ≠ 0 d = a 8 So, 2 n d term, 5 t h term, 9 t h term would be a + a 8 , a + a 2 , a + a 9 a 8 , 3 a 2 , 2 a Common Ratio = 2 n d t e r m 1 s t t e r m = 3 a × 8 2 × 9 a = 4 3

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