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

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.

$\therefore a_{8}=a r^{8-1}=a r^{7}$

$\Rightarrow a r^{7}=192$

$a(2)^{7}=192$

$a(2)^{7}=(2)^{6}(3)$

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

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

 

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