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

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Aicharya · Accepted Answer

Let the A.P. be a , &#160; a + d , &#160; a + 2 d , &#160; . . . . . 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 &#8757; d &#160; &#8800; 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 &#160; Common Ratio = 2 n d &#160; t e r m 1 s t &#160; t e r m = 3 a &#215; 8 2 &#215; 9 a &#160; = 4 3

If the 2 n d , 5 t h and 9 t h terms of a non-constant arithmetic progression are in geometric progression,…

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