The correct option is C 1022 This is G.P in which #160; a=2,r=2^22=2 and n=9 ∴ S_n=a(r^n 1)(r 1)=2× (2^9 1)(2 1)=2× (512 1)=2× 511 ...

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Geometric Progression

2+22+23+........

Question

$2 + 2^{2} + 2^{3} + . . . . . . . + 2^{9} =$ ?

2044

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1022

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1056

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None of these

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Solution

The correct option is C $1022$
This is G.P in which $a = 2, r = \frac{2^{2}}{2} = 2$ and $n = 9$
$∴$ $S_{n} = \frac{a (r^{n} - 1)}{(r - 1)} = \frac{2 \times (2^{9} - 1)}{(2 - 1)} = 2 \times (512 - 1) = 2 \times 511 = 1022$ .

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