Find the indicated sums for the following Geometric Progression.
$1, \sqrt{2}, 2, . . . . . . . . . .$ Find $S_{10}$

31 (\sqrt{2} - 1)

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31 (\sqrt{2} + 1)

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32 (\sqrt{2} + 1)

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32 (\sqrt{2} - 1)

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Solution

The correct option is B $31 (\sqrt{2} + 1)$
Clearly, the given GP has first term $a = 1$ and common ratio $r = \sqrt{2} .$
$∴ S_{10} = a \times (\frac{r^{10} - 1}{r - 1}) = 1 \times (\frac{(\sqrt{2})^{10} - 1}{\sqrt{2} - 1})$

= $\frac{31}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}$

= $\frac{31 \times (\sqrt{2} + 1)}{2 - 1}$

= $31 (\sqrt{2} + 1)$

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Find the indicated sums for the following Geometric Progression.1,√2,2,.......... Find S10

The correct option is B 31(√2+1)Clearly, the given GP has first term a=1 and common ratio r=√2.∴ S10=a×(r10−1r−1)=1×((√2)10−1√2−1) =31√2−1×√2+1√2+1 =31×(√2+1)2−1 =31(√2+1)

Find the indicated sums for the following Geometric Progression.
$1, \sqrt{2}, 2, . . . . . . . . . .$ Find $S_{10}$