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Q.

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

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a

$\frac{7}{4}$

b

$\frac{8}{5}$

c

$\frac{4}{3}$

d

$1$

answer is C.

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Detailed Solution

$a + d, a + 4 d, a + 8 d$ are in G.P.

$\begin{array}{l} \Rightarrow {(a + 4 d)}^{2} = (a + d) (a + 8 d) \\ \Rightarrow a^{2} + 16 d^{2} + 8 d a = a^{2} + 9 a d + 8 d^{2} \\ \Rightarrow 8 d^{2} - a d = 0 \\ \Rightarrow d (8 d - a) = 0 \\ \Rightarrow a = 8 d \\ ∴ r = \frac{a + 4 d}{a + d} = \frac{12 d}{9 d} = \frac{4}{3} \end{array}$

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