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

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Solution

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Common ratio, $r=2$ Let $a$ be the first term of the G.P. $∴a_{8}=ar_{8−1}=ar_{7}⇒ar_{7}=192⇒a(2)_{7}=192⇒a(2)_{7}=(2)_{6}(3)⇒a=(2)_{7}(2)_{6}×3 =23 ∴a_{12}=ar_{12−1}=(23 )(2)_{11}=(3)(2)_{16}=3072$