Question

Find the average of first $40$ natural numbers.

Answer 1

Find the average of first $40$ natural numbers.

Average of a given set of numbers is calculated as $\frac{1}{n}\sum _{i=1}^n{a}_i$, where $n$ is the number of values and $a_i$ is the data value.

First $40$ natural numbers are:

$1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,....,40$

Average of these numbers is:

$\begin{array}{rcl}\frac{1+2+3+4+5+6+7+8+9+....+40}{40}& =& \frac{{\displaystyle \frac{40(40+1)}{2}}}{40}[\mathrm{Sum}\mathrm{of}\mathrm{first}\text{'}\mathrm{n}\text{'}\mathrm{natural}\mathrm{numbers}=\frac{n(n+1)}{2}]\\ & =& \frac{820}{40}\\ & =& 20.5\end{array}$

Hence, the average of first $40$ natural numbers is $20.5$.