Question

Write the sum of first n odd natural numbers.

Answer 1

We have,

1 + 3 + 5 + ... up to n terms

$\therefore S_n=\frac{n}{2}[2\times 1+(n-1)\times 2]$ $[\because S_n=\frac{n}{2}[2a+(n-1)d\left]\right]$

$=\frac{n}{2}[2+2n-2]$

$=\frac{n}{2}\times 2n$

$=n^2$

$\therefore$ 1 + 3 + 5 + ... up to n terms $=n^2$

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