Question

Fifth term of a GP is $2$, then the product of its $9$ terms is

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

Answer 1

The correct option is B

$512$

Given, $a_5=2$

Find the product of first $9$ terms of given GP:

As we know,

$a,ar,a{r}^2,a{r}^3,a{r}^4,a{r}^5,a{r}^6,a{r}^7,a{r}^8$ are the $9$ terms of GP

Here, $a_5=a{r}^4$

$\Rightarrow$ $a{r}^4=2$

Now, product of first $9$ terms is

$=a\times ar\times a{r}^2\times a{r}^3\times a{r}^4\times a{r}^5\times a{r}^6\times a{r}^7\times a{r}^8$

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

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

$=2^9$

$=\mathbf{512}$

Hence, Option ‘B’ is Correct.