Question

The arithmetic mean of first n odd natural numbers is

• A. $\frac{2^n}{(n+1)}$
• B. $\frac{2^n}{n}$
• C. $\frac{2^n-1}{(n+1)}$
• D. n

Answer 1

The correct option is D n

$Thefirstnoddnaturalnumbersare1,3,5,....(2n-1)sumofthesenumbers\sum x=1+3+5+.....+(2n-1)=\frac{n}{2}[1+(2n-1\left)\right]=\frac{n}{2}\left(2n\right)=n^{2}Thus,\overline{x}=\frac{1}{n}\sum x=\frac{n^2}{n}=n$