Question

Fifth term of a G.P. 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 $512$

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

To calculate: $a_5=a{r}^{n-1}$

$a{r}^4=\mathrm{2.....}given$

Now, product of first 9 terms :

$a\times ar\times a{r}^2\times a{r}^3\times a{r}^4\times a{r}^5\times a{r}^6\times a{r}^7\times a{r}^8=a^9{r}^{36}=(a{r}^4{)}^9=2^9=512$