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.