Average of n numbers is a. The first number is increased by 2, second one is increased by 4, the third one is increased by 8 and so on. The average of the new number is

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$a + 2 \cdot \frac{2^{n} - 1}{n}$

$a + \frac{2^{n} - 1}{n}$

$a + 2 \cdot \frac{2^{n} + 1}{n}$

$a + \frac{2^{n + 1} - 1}{n}$

answer is A.

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Detailed Solution

Average $= \frac{n a + 2 + 4 + 8 + \dots . + 2^{n}}{n}$

$= \frac{n a + 2 (\frac{2^{n} - 1}{2 - 1})}{n} = a + 2 \cdot \frac{2^{n} - 1}{n}$

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