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If the 2nd, 5 th and 9th terms of a non-constant AP are in GP., then the common ratio of this GP is

$\frac{8}{5}$

$\frac{4}{3}$

C) 1

$\frac{7}{4}$

Option B

Let a be the first term and d be the common difference. Then , we have a+d, a+4d, a+8d in GP

i.e., (a+4d)² = (a+d)(a+8d)

$\Rightarrow a^{2}+16d^{2}+8ad= a^{2}+8ad+ad+8d^{2}$

$\Rightarrow 8d^{2}=a d$

$\Rightarrow 8d=a$ [ d≠ 0]

Now,

common ratio

$r=\frac{a+4d}{a+d}$

$=\frac{8d+4d}{8d+d}$

$=\frac{12d}{9d}$ = $\frac{4}{3}$

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