Question

The mean of first n odd natural numbers is _________.

Answer 1

The first n odd natural numbers are 1, 3, 5, ..., 2n − 1.

This forms an AP with a = 1 and l = 2n − 1.

Sum of first n odd natural numbers $=\frac{n}{2}\left(1+2n-1\right)=n^2\left[S_n=\frac{n}{2}\left(a+l\right)\right]$

∴ Mean of first n odd natural numbers$=\frac{\mathrm{Sum}\mathrm{of}\mathrm{first}n\mathrm{odd}\mathrm{natural}\mathrm{numbers}}{n}=\frac{n^2}{n}=n$

The mean of first n odd natural numbers is ____n____.