Question

If $3^{rd}$ term of a G.P is 12 and $6^{th}$ term is 96, then its $7^{th}$ term is .

• A. 288
• B. 192
• C. 182
• D. 144

Answer 1

The correct option is B 192

To find the $7^{th}$ term, we need the common ratio and the first term.

We will use the given two conditions to find them.

$T_3=12$

$\Rightarrow a{r}^2=12$ ... (1)

$t_6=96$

$\Rightarrow a{r}^5=96$ ... (2)

Dividing (2) by (1), we get,
$\Rightarrow r^3=\frac{96}{12}=8$

$\Rightarrow r=2$

$a{r}^2=12$

$a\times 2^2=12$

$\Rightarrow a=3$

$T_7=a{r}^{7-1}$

$=3\times 2^6=64\times 3=192$