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Formula for Sum of n Terms of an AP

The sum of ...

Question

The sum of $p$ terms of G.P. whose $p^{t h}$ term is $2^{p}$ is

2 (2^{p} - 1)

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2 (2^{p + 1} - 1)

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2 (2^{p} + 2)

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2 (2^{p + 1} + 2)

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Solution

The correct option is B $2 (2^{p} - 1)$
Let $T_{p}$ be the pth term of $G . P$ .
Then
$T_{p} = A R^{p - 1} = 2^{P}$ where first term = $A$ and Common ratio= $R$
So by comparing I can assume that $A = 2$ and $R = 2$
So $S_{P} = A \frac{R^{p} - 1}{R - 1} = 2 (2^{p} - 1)$
Hence the correct option is A

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List-I (Electronic configuration of elements )	List-II (I.E. in kJ/mol)
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