Question

Without adding, find the sum.

$\text{1+3+5+7+9+11+13+15+17+19+21+}23$

Answer 1

Find the sum without adding.

The sum of first $n$ odd numbers together without actually adding them individually is $n^2$.

It can be observed that the here the sum of first $12$ odd natural numbers is to be calculated.

Thus,

$n=12$

So, the sum is,

$\begin{array}{rcl}\text{1+3+5+7+9+11+13+15+17+19+21+}23& =& {12}^2\\ & =& 144\end{array}$

Thus, the sum is $144$.