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The sum of $20$ terms in the $G . P$ $0.15, 0.015, 0.0015 .....$ is

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\frac{1}{6} (1 - {(0.1)}^{20})

1 - {(0.1)}^{20}

none of these

\frac{1}{6} (1 + {(0.1)}^{20})

answer is A.

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Detailed Solution

a = 0.15, r = \frac{0.015}{0.15} = 0.1

$S_{n} = \frac{a (1 - r^{n})}{1 - r} = \frac{0.15 (1 - {(0.1)}^{20})}{1 - 0.1}$

$= \frac{0.15}{0.9} (1 - {(0.1)}^{20})$

$= \frac{15}{90} (1 - {(0.1)}^{20})$

$= \frac{1}{6} (1 - {(0.1)}^{20})$

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