Question

If 6th term of GP is $2$, then the product of first $11$ terms of the GP is equal to

• A. $512$
• B. $1024$
• C. $2048$
• D. $256$
• E. $32$

Answer 1

The correct option is C $2048$

$11$ terms of GP are
$\because a{r}^5,a{r}^4,a{r}^3,a{r}^2,ar,a,\frac{a}{r},\frac{a}{r^2},\frac{a}{r^3},\frac{a}{r^4},\frac{a}{r^5}$
6th term of GP$=2$

$\because$ $a=2$

$\therefore$ Product of first $11$ terms

$a{r}^5\times a{r}^4\times a{r}^3\times a{r}^2\times ar\times a\times \frac{a}{r}\times \frac{a}{r^2}\times \frac{a}{r^3}\times \frac{a}{r^4}\times \frac{a}{r^5}$

$=a^{11}=2^{11}=2048$