Question

Study the following pattern and find the sum of first 12 odd numbers :

$$\begin{gathered} 1^2=1 \\ {2}^2=1+3 \\ {3}^2=1+3+5 \\ {4}^2=1+3+5+7 \end{gathered}$$

Answer 1

In order to find the sum of first 12 odd numbers, we will continue the pattern and observe how the sum of odd numbers are related to squares of numbers.

In $1^2$ number in right hand side is one,

In $2^2$ there are two odd numbers,

In $3^2$ there is the sum of first three odd numbers,

Hence for the sum of first $12$ odd numbers, ${12}^2$ will be there on the left hand side in the pattern.

$\Rightarrow Thereforesumoffirst12oddnumbers={12}^2=144$.