Question

The third term of a G.P is the square of first term. If the second term is $8$, then the $6^{th}$ term is

• A. $120$
• B. $124$
• C. $128$
• D. $132$

Answer 1

The correct option is C

$128$

Calculating the $6^{th}$ term:

Let $a,ar,a{r}^2$ in the GP.

Given : $a{r}^2=a^2$ and $ar=8$

Thus $r^2=a$

$\Rightarrow$ $r^3=8$

$\Rightarrow$ $r=2$

and $a=4$

Since $6^{th}$ term is given by $a{r}^5$,

$\begin{array}{rcl}{a}_6& =& a{r}^5\\ & =& 4{\left(2\right)}^5\\ & =& 4\left(32\right)\\ & =& 128\end{array}$

Therefore,$6^{th}$ term of the G.P. is $128$.

Hence, option (c) is the correct option.