Question

The arithmetic mean of the first $n$ natural numbers is

• A. $\frac{(n+1)}{2}$
• B. $\frac{(n-1)}{2}$
• C. $\frac{n}{2}$
• D. None of these

Answer 1

The correct option is A $\frac{(n+1)}{2}$

First $n$ natural numbers are, $1,2,3,..........n$

Sum of these numbers $=1+2+3+.....+n=\frac{n(n+1)}{2}$

Hence arithmetic mean $=\frac{\text{Sum of numbers}}{\text{Total numbers}}=\frac{\frac{n(n+1)}{2}}{n}=\frac{n+1}{2}$