Question

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

Answer 1

The sequence of first $n$ odd numbers is

$1,3,5,\mathrm{7.........}n$

This forms an A.P with $a=1$ and $d=2$

$S=\frac{n}{2}\{2a+(n-1\left)d\right\}\Rightarrow S=\frac{n}{2}\left\{2\right(1)+(n-1\left)2\right\}\Rightarrow S=\frac{n}{2}\left(2n\right)\Rightarrow S=n^2$