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

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8. Sequences and Series

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

A

$3072$

B

$3072$

C

$3072$

D

$3072$

Solution

Common ratio, $r =2$

Let $a$ be the first term of the $G.P.$

$\therefore a_{8}=a r^{s-1}=a r^{7} \Rightarrow a r^{7}=192 \Rightarrow a(2)^{7}=192 \Rightarrow a(7)^{7}=(2)^{6}(3)$

$\Rightarrow a=\frac{(2)^{6} \times 3}{(2)^{7}}=\frac{3}{2}$

$\therefore a_{12}=a r^{12-1}=\left(\frac{3}{2}\right)(2)^{11}=(3)(2)^{10}=3072$

Standard 11

Mathematics

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