Let a, b and c form a GP of common ratio r, with 0< r<1. If a, 2b and 3c form an AP, then r equals


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Question Number 56420 by gunawan last updated on 16/Mar/19

$Let a, b and c form a GP of common ratio r,$ $with 0 < r < 1 . If a, 2 b and 3 c form an AP,$ $then r equals$
	Answered by tanmay.chaudhury50@gmail.com last updated on 16/Mar/19

	$a = a$ $b = a r$ $c = {a r}^{2}$ $2 (2 b) = a + 3 c$ $2 (2 a r) = a + 3 ({a r}^{2})$ $4 r = 1 + 3 r^{2}$ $3 r^{2} - 3 r - r + 1 = 0$ $3 r (r - 1) - 1 (r - 1) = 0$ $(r - 1) (3 r - 1) = 0$ $r \neq 1 [g i v e n i n q u e s t i o n]$ $r = \frac{1}{3}$
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