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:

• A. 1
• B. $\frac{7}{4}$
• C. $\frac{8}{5}$
• D. $\frac{4}{3}$

Answer 1

The correct option is D $\frac{4}{3}$

Let the GP be a, ar, and $a{r}^2$ then a = A + d; ar = A + 4d;$a{r}^2=A+8d$
$\Rightarrow \frac{a{r}^2-ar}{ar-a}=\frac{(A+8d)-(A+4d)}{(A+4d)-(A+d)}$
$r=\frac{4}{3}$