The arithmetic mean of the series 1, 2, 4, 8, 16, . . . . . . , $2^{n}$ is.
A. $\Large\frac{2^{n}-1}{n+1}$ B. $\Large\frac{2^{n}+1}{n}$ C. $\Large\frac{2^{n}-1}{n}$ D. $\Large\frac{2^{n+1}-1}{n+1}$ Answer: Option DShow Answer
Solution(By Apex 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
$\begin{array}{l}=\Large\frac{2^{n+1}-1}{2-1}\\
=2^{n+1}-1\\
\text{ Arithmetic mean }\\
=\Large\frac{2^{n+1}-1}{n+1}\end{array}$
