If the 2nd, 5th and 9th terms of a non constant A.P. are in G.P., then the common ratio of this G.P. is

Engineering

Mathematics

Geometric Progression and Its Properties

Question

If the 2^nd, 5^th and 9^th terms of a non constant A.P. are in G.P., then the common ratio of this G.P. is

$\frac{4}{3}$

$\frac{7}{4}$

$\frac{8}{5}$

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Let a, ar, ar² be the three consecutive terms of GP and d be the common difference of AP
$∴$ ar – a = 3d
and ar² – ar = 4d

$\Rightarrow \frac{ar - a}{3} = \frac{{ar}^{2} - ar}{4}$

$\frac{(r - 1)}{3} = \frac{r (r - 1)}{4} \Rightarrow r = \frac{4}{3}$