Question

Write the sum of first n odd natural numbers.

Answer 1

We need to find the sum of 1, 3, 5, 7... upto n terms.
Here, a = 1, d = 2

We know:
$$\begin{gathered} S_n=\frac{n}{2}\left\{2a+\left(n-1\right)d\right\} \\ =\frac{n}{2}\left\{2\times 1+\left(n-1\right)2\right\} \\ =n^2 \end{gathered}$$

Therefore, the sum of the first n odd numbers is $n^2$.