Complete the conjecture.
The sum of the first n odd positive integers is ____.

The correct answer is: The sum of first n odd natural numbers is n2.

To find the sum of arithmetic progression, we have to know the first term, the number of terms and the common difference between each term. Then use the formula given below:

S = n/2[2a + (n − 1) × d]
To find: Sum of first n odd natural numbers
The first n odd natural numbers are given by 1,3,5,7,9…… (2n – 1) and this forms an AP.

• a = 1
• d = 2
• t_n = (2n – 1)

The formula of sum of an A.P series

S = n/2[2a + (n − 1) × d]

S = n /2 [2 + 2n – 2]

S = n /2 [2n]

S = n²
The sum of first n odd natural numbers is n².