Question:
Find the $12^{\text {th }}$ term of a G.P. whose $8^{\text {th }}$ term is 192 and the common ratio is $2 .$
Solution:
Common ratio, $r=2$
Let a be the first term of the G.P.
$\therefore a_{8}=a r^{8-1}=a r^{7}$
$\Rightarrow a r^{7}=192$
$a(2)^{7}=192$
$a(2)^{7}=(2)^{6}(3)$
$\Rightarrow a=\frac{(2)^{6} \times 3}{(2)^{7}}=\frac{3}{2}$
$\therefore a_{12}=a r^{12-1}=\left(\frac{3}{2}\right)(2)^{11}=(3)(2)^{10}=3072$