The sum of first n odd natural numbers in

Solution (By Examveda Team)

1, 3, 5, 7, ........ are n odd numbers
Where a = 1, and d = 2
$$\eqalign{ & \therefore {S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{n}{2}\left[ {2 \times 1 + \left( {n - 1} \right) \times 2} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{n}{2}\left[ {2 + 2n - 2} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{n}{2} \times 2n \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {n^2} \cr} $$