Question

The sum of first n odd natural numbers is__________

Answer 1

Answer:

The first n odd natural numbers are 1, 3, 5, ... 2n-1. This forms an arithmetic progression with first term 1, common difference 2 and last term (2n-1). The sum is given by S = 1+3+5+...

Answer 2

Odd natural numbers are 1 , 3 , 5 , 7 , 9 , 11 , ......

Here ,

                First term , a = 1

Common difference , d = 3-1 = 2

Now odd natural numbers are in arithmetic progression .

$\implies \bold{S_n=\frac{n}{2}[2a+(n-1)d] }\\\\\implies \bold{S_n=\frac{n}{2}[2(1)+(n-1)2] }\\\\\implies \bold{S_n=\frac{n}{2}[2+2n-2] }\\\\\implies \bold{\bf{\blue{S_n=n^2}}}$

So the sum of first n odd natural numbers are  " n² "