Question

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

• A. $n^3$
• B. $n(n+1)$
• C. $n(n+1{)}^2$
• D. $n^2$

Answer 1

The correct option is D $n^2$

We have to find sum of the series : $1+3+5+...$ to $n$ terms
Clearly, terms of the given series form an AP with first term $a=1$ and common difference $d=2$.

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

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