Question

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

• A. $4^3$
• B. $4^5$
• C. $4^4$
• D. None of these

Answer 1

Answer: (B)

$4^5$

Let the common ratio be $r$ and the terms be $a,ar,a{r}^2,a{r}^3,a{r}^4$ and so on in G.P.

Also, given that the third term is 4.

$\Rightarrow a{r}^2=4$ $...\left(1\right)$

Therefore, the product of the first five term is given by,

$a\cdot ar\cdot a{r}^2\cdot a{r}^3\cdot a{r}^4=a^5{r}^{10}$

$\Rightarrow a\cdot ar\cdot a{r}^2\cdot a{r}^3\cdot a{r}^4={\left(a{r}^2\right)}^5$

From equation $\left(1\right)$, substitute $a{r}^2=4$; we get

$a\cdot ar\cdot a{r}^2\cdot a{r}^3\cdot a{r}^4=4^5$

Thus, the product of the first five term is $4^5$.