Question:
Find the sum of first n odd natural numbers.
Solution:
The first n odd natural numbers are:
1, 3, 5, 7, 9...
a = 1, d = 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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