Subject: General Aptitude · Chapter: Average · Exam: · Marks: · Difficulty:
The arithmetic mean of the series 1, 2, 4, 8, 16,..., $2^{n}$ 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
Answer (as printed): D
Explanation
The given series is a G.P. with first term, $a=1$ and common ratio, $r=2$. It has $(n+1)$ terms. $$\text { ∴ Sum of the terms of the series }=\frac{\left(2^{n+1}-1\right)}{(2-1)}=2^{n+1}-1 .$$ Arithmetic mean $=\frac{2^{n+1}-1}{n+1}$.
Explanation as extracted from the printed page; notation may be imperfect.