Question

If the third term of a G.P is $4$ then the product of its first $5$ terms is

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

Answer 1

The correct option is C

$4^5$

Explanation for the correct option:

Finding the product of first $5$ terms:

The $n^{\mathrm{th}}$ term of a G.P. is $a{r}^{\mathrm{n}-1}$.

The third term of a G.P is $4$.

$a{r}^2=4$

So, The product of the first $5$ terms is,

$\begin{array}{rcl}a\left(ar\right)\left(a{r}^2\right)\left(a{r}^3\right)\left(a{r}^4\right)& =& a^5{r}^{10}\\ & =& {\left(a{r}^2\right)}^5\\ & =& 4^5;\left[\mathrm{from}1\right]\end{array}$

Hence, the correct option is C.