Question

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

Answer 1

Find the sum of the A.P. by using the formula.

The first $n$ odd natural numbers are given by $1,3,5,7,9\dots \dots (2n–1)$ and this forms an AP.

The first term,$a=1$

The common difference, $d=2$

The formula for sum of an A.P series

$$\begin{gathered} \Rightarrow S=\frac{n}{2}[2a+(n-1)\times d] \\ \Rightarrow S=\frac{n}{2}[2+2n–2] \\ \Rightarrow S=\frac{n}{2}\left[2n\right] \\ \Rightarrow S=n^2 \end{gathered}$$

Hence, the sum of the first $n$ odd natural numbers is $n^2$.