Question

The $4^{th}$ and the $9^{th}$ term of a G. P. are 8 and 256 respectively. Find the G. P.

• A. 1, 9, 15, 20, 26
• B. 1, 3, 5, 8, 16
• C. 1, 2, 4, 8, 16
• D. 2, 4, 8, 16, 36

Answer 1

The correct option is C

1, 2, 4, 8, 16

Let 'a' be the first term and r be the common ratio of the G. P, then

$t_4$ = $a{r}^{4-1}$ = $a{r}^3$

$t_9$ = $a{r}^{9-1}$ = $a{r}^8$

According to the question, $a{r}^8$ = $256$------- (1)

and $a{r}^3$ = $8$ ------- (2)

∴ $\frac{a{r}^8}{a{r}^3}$ = $\frac{256}{8}$

or $r^5$ = $32$ = $2^5$

∴ r = 2

Again from (2), a $\times$ $2^3$ = $8$

∴ a = $\frac{8}{8}$ = $1$

Therefore, the G. P. is 1, 2, 4, 8, 16,......