The arithmetic mean of the series 1, 2, 4, 8, 16, . . . . . . , 2ⁿ is -

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

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

C. $$\frac{{{2^n} - 1}}{{n}}$$

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

Answer: Option D

Solution(By Examveda Team)

The given series is a G.P. with first term, a = 1 and common ratio, r = 2,
It has (n + 1) terms.
∴ Sum of the terms of the series
= $$\frac{{{2^{n + 1}} - 1}}{{2 - 1}}$$
= 2^{n + 1} $$ - $$ 1
Arithmetic mean = $$\frac{{{2^{n + 1}} - 1}}{{n + 1}}$$