Maths-

General

Easy

Question

# Complete the conjecture.

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

Hint:

### A sequence of numbers which has a common difference between any two consecutive numbers is called an arithmetic progression (A.P.). The arithmetic progression general form is given by a, a + d, a + 2d, a + 3d, . . .. Hence, the formula to find the nth term is:

an = a + (n – 1) × d

## 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 = n^{2}

The sum of first n odd natural numbers is n^{2}.

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.

_{n}= (2n – 1)^{2}

The sum of first n odd natural numbers is n

^{2}.

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