Find the sum of first n odd natural numbers.


Find the sum of first n odd natural numbers.


The first n odd natural numbers are:

1, 3, 5, 7, 9...

a = 1, = 2, Total terms = n

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

$\Rightarrow S_{n}=\frac{n}{2}[2 \times 1+(n-1) 2]$

$\Rightarrow S_{n}=\frac{n}{2}[2+(n-1) 2]$

$\Rightarrow S_{n}=\frac{n}{2}[2 n]$

$\Rightarrow S_{n}=n^{2}$



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