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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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2012

2020

3070

3072

answer is D.

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Detailed Solution

$r = 2$

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

$a r^{7} = 192$

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

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

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

$a_{12} = a r^{11} = (\frac{3}{2}) \times 2^{11} = 3072$ .

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