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The number of terms in the G.P 6, 12, 24, ..., 1536 is

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answer is D.

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Detailed Solution

$a_{1} = 6, a_{2} = 12; a_{3} = 24; a_{n} = 1536$

$r = \frac{a_{2}}{a_{1}} = \frac{12}{6} = 2$

$1536 = (6) {(2)}^{n - 1}$

$\begin{array}{l} 256 = {(2)}^{n - 1} \\ 2^{8} = 2^{n - 1} \\ 8 = n - 1 \\ n = 9 \end{array}$

Hence, 1536 is the 9^th term

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