Question

Find the sum without actually adding it.

$1+3+5+7+9+11+13+15+17+19+21$

• A. $101$
• B. $161$
• C. $121$
• D. $141$

Answer 1

The correct option is C $121$

Given series is $1+3+5+7+9+11+13+15+17+21$

Sum of first odd natural numbers $=n^2$

where $n=$ number of odd numbers

Here, $21$ is the ${11}^{th}$ odd number. Thus $n=11$

So, sum of the series given $={11}^2=121$.