Average of n numbers is a. Thefirst 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

A

$$ a + 2  \frac{2^n - 1}{n} $$

B

$$ a +  \frac{2^n - 1}{n} $$

C

$$ a + 2  \frac{2^n + 1}{n} $$

D

$$ a + 2  \frac{2^{n+1} - 1}{n} $$