Find the sum of first n odd natural numbers. - Vidyadip

Question

Find the sum of first $n$ odd natural numbers.

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Answer

In this problem, we need to find the sum of first $n$ odd natural numbers.
So, we know that the first odd natural number is $1.$ Also, all the odd terms will form an $A.P.$ with the common difference of $2.$
So here,
First term $(a) = 1$
Common difference $(d) = 2$
So, let us take the number of terms as $n$
Now, as we know,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$
So, for n terms,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2(1)+(\text{n}-1)2]$
$=\frac{\text{n}}{2}[2+2\text{n}-2]$
$=\frac{\text{n}}{2}(2\text{n})$
$=\text{n}^2$
Therefore, the sum of first $n$ odd natural numbers is $S_n=n^2$.

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