Question

Express $144$ as a sum of $12$ odd numbers.

Answer 1

We know that the sum of the first $n$ odd natural numbers is equal to $n^2$, for every natural number $n$.

Therefore, the sum of first $12$ odd natural numbers is equal to ${12}^2=144$.

Now, the first $12$ odd numbers are $1,3,5,7,9,11,13,15,17,19,21,23$ and their sum is determined as follows:

$1+3+5+7+9+11+13+15+17+19+21+23={12}^2=144$

Hence $1+3+5+7+9+11+13+15+17+19+21+23=144$