Question

The sum of first n odd natural numbers is ________.

Answer 1

First n odd natural numbers are: 1, 3, 5, 7, ...

First term (a) = 1
Common difference (d) = 3 – 1 = 2

Now,
$$\begin{gathered} S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right] \\ =\frac{n}{2}\left[2\left(1\right)+\left(n-1\right)\left(2\right)\right] \\ =\frac{n}{2}\left[2+2n-2\right] \\ =\frac{n}{2}\left[2n\right] \\ =n^2 \end{gathered}$$

Hence, the sum of first n odd natural numbers is n².