Question

The third term of a G.P. is $4$. The product of the first five terms is

Answer 1

Find the product of first five term

Let $a$ be the first term of G.P. and $r$ be the common ratio.

Given : Third term of a G.P. is $4$, i.e $a{r}^2=4$.

Since the product of the first five terms is given by,

$\therefore a·\left(ar\right)·\left(a{r}^2\right)·\left(a{r}^3\right)·\left(a{r}^4\right)$

$$\begin{gathered} =a^5{r}^{10} \\ ={\left(a{r}^2\right)}^5 \\ =4^5\left[\because a{r}^2=4\right] \\ =1024 \end{gathered}$$

Hence the product of the first five term of G.P. is $1024$.