Question

What is the arithmetic mean of first $n$ natural numbers?

Answer 1

Arithmetic Mean: An arithmetic mean is the ratio of the sum of the numbers to the total number of numbers.

The first $n$ natural numbers are: $1,2,3,4,5,....,n$

We know that, the sum of the first $n$ natural numbers $=\frac{n\left(n+1\right)}{2}$

So, the arithmetic mean of first $n$ natural numbers is,

$arithmeticmean=\frac{\frac{n\left(n+1\right)}{2}}{n}$

$\Rightarrow$$arithmeticmean=\frac{n\left(n+1\right)}{2n}$

$\Rightarrow$$arithmeticmean=\frac{\left(n+1\right)}{2}$

Hence, the arithmetic mean of first $n$ natural numbers is $\frac{\left(n+1\right)}{2}$.