Question

If the $3^{\text{rd}}$ term of a G.P is 4, then the product of its first five terms is .

• A. 512
• B. 1024
• C. 128

Answer 1

The correct option is B 1024

Let the first term of the G.P. be $a$ and its common ratio be $r$
Since the $n^{\text{th}}$ term of such a GP is given by $a_n=a{r}^{n-1},$ we have
$a_3=a{r}^2=4.$
Now,
$\text{product of first five terms}=a\times ar\times a{r}^2\times a{r}^3\times a{r}^4$
$=a^5{r}^{10}$
$=(a{r}^2{)}^5$
$=4^5$
$=1024$