Question

If fifth term of a GP is $2$, then the product of its first $9$ terms is:

• A. $256$
• B. $512$
• C. $1024$
• D. None of these

Answer 1

The correct option is B $512$

Let the first term of G.P. $=a$

The common ratio be $r$

Then, $a{r}^4=2$

Product of first nine terms $=$ $a\times ar\times a{r}^2\times a{r}^3\times a{r}^4\times a{r}^5\times a{r}^6\times a{r}^7\times a{r}^8$

$=$ $a^9{r}^{36}$

$=$ ${\left(a{r}^4\right)}^9$

$=$ $2^9$

$=512$