Answer:
Given,
AP of first n odd natural numbers whose first term a is 1
Common difference d = 3
The sequence is 1, 3, 5, 7……n
a = 1, d = 3-1 = 2, n = n
By using the formula,
S = n/2 [2a + (n-1)d]
S = n/2 [2(1) + (n-1)2]
S = n/2 [2 + 2n – 2]
S = n/2 [2n]
S = n2
∴ The sum of the first n odd natural numbers is n2.