The arithmetic mean of first n natural numbers

Question:

The arithmetic mean of first n natural numbers is ___________.

Solution:

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

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

Hence arithmetic mean of first $n$ natural numbers $=\frac{\text { Sum of numbers }}{\text { Total numbers }}$

$=\frac{n(n+1) / 2}{n}$

i.e Arithmetic mean of first $n$ natural number $=\frac{n+1}{2}$

 

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