Question

Find the ${12}^{th}$ term of a $G.P.$ whose $8^{th}$ term is $192$ and the common ratio is $2$.

Answer 1

Given, common ratio $=r=2$ and $8^{th}$ term is $192$

Step$:1$ Finding the value of first term $a$.
We know, the $n^{th}$ term of $G.P.$ is
$a_n=a{r}^{n-1}$
$\Rightarrow 192=a\times 2^{8-1}$
$\Rightarrow 192=a\times 2^7$
$a=\frac{3}{2}\cdots \left(i\right)$

Step$:2$ Finding ${12}^{th}$ term of a $G.P.$
$a_{12}=a{r}^{12-1}$
$\Rightarrow a_{12}=a{r}^{11}$
$\Rightarrow a_{12}=\frac{3}{2}\times 2^{11}$
$\Rightarrow a_{12}=3\times 2^{10}$
$\Rightarrow a_{12}=3\times 1024$
$\therefore a_{12}=3072$

Hence, ${12}^{th}$ term is $3072$.