Question

The mean of first n odd natural number is

(a) $\frac{n+1}{2}$
(b) $\frac{n}{2}$
(c) n
(d) n²

Answer 1

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

∴ Mean of first n odd natural numbers

$$\begin{gathered} =\frac{1+3+5+...+\left(2n-1\right)}{n} \\ =\frac{{\displaystyle \frac{n}{2}}\left(1+2n-1\right)}{n}\left[S_n=\frac{n}{2}\left(a+l\right)\right] \\ =\frac{2n}{2} \\ =n \end{gathered}$$

Hence, the correct answer is (c).