Sequence of odd natural numbers is
1, 3, 5, 7, …
This sequence is an A.P. with
a = 1, d = 3 – 1 = 2
\(\therefore\) The sum of first n odd natural numbers is n2.
Sequence of even natural numbers is
2, 4, 6, 8, …
This sequence is an A.P. with
a = 2, d = 4 – 2 = 2
\(\therefore\) The sum of first n even natural numbers is n(n + 1).
