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

Answer: Option D

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