Question

The arithmetic mean of first n natural numbers is ___________.

Answer 1

First n natural numbers are 1, 2, 3, ...........n
Sum of these numbers is 1 + 2 + 3 + ........... + n $=\frac{n\left(n+1\right)}{2}$

$\begin{array}{rcl}\mathrm{Hence}\mathrm{arithmetic}\mathrm{mean}\mathrm{of}\mathrm{first}\mathit{}n\mathrm{natural}\mathrm{numbers}& =& \frac{\mathrm{Sum}\mathrm{of}\mathrm{numbers}}{\mathrm{Total}\mathrm{numbers}}\\ & =& \frac{n\left(n+1\right)/2}{n}\end{array}$
i.e Arithmetic mean of first n natural number = $\frac{n+1}{2}$