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