Question

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

Answer 1

Let ${}^{\prime }{a}^{\prime }$ be the first term of given G.P.

Here $r=2$ and $A^8=192$

$a{r}^{8-1}=192\Rightarrow a\times (2{)}^7=192$

$\Rightarrow a=\frac{192}{128}\Rightarrow a=\frac{3}{2}$

Now, $a_{12}=a{r}^{12-1}=\frac{3}{2}\times (2{)}^n=3\times 2^{10}$

= $3\times 1024=3072.$
Therefore, ${12}^{th}$ term of given G.P is $3072.$