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 numbers is -

A. $$a + \frac{{2\left( {{2^n} - 1} \right)}}{n}$$

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

C. $$a + \frac{{{2^{n + 1}}}}{n}$$

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

Answer: Option A

Solution(By Examveda Team)

Series:- a, a + 2, a + 4.....
Sum = na + 2 + 4 + ..... upto n terms
Sum = na + S_n
$${S_n} = \frac{{2\left( {{2^n} - 1} \right)}}{{2 - 1}}$$
Average = $$a + \frac{{2\left( {{2^n} - 1} \right)}}{n}$$