Question

find the sum of first n term of odd natural number​

Answer 1

Answer:

n²

Step-by-step explanation:

The sum of first n terms of odd natural number is given by n²

eg. 1+3+5 = 3² = 9

     1+3+5+7+9+11 = 6² = 36

Answer 2

SOLUTION:

Natural Odd numbers = 1, 3, 5, 7,.....

3 - 1 = 2 , 5 - 3 = 2....

As, common difference is same. Then it forms as an AP.

AP = 1, 3, 5, 7.......

First term = a = 1

Common Difference = d = 2

We know that,

In an AP, sum of n terms is n/2 [ 2a + (n - 1)d ]

Sn = n/2 [ 2(1) + (n - 1)2

= n/2 [ 2 + 2n - 2 ]

= n/2 [ 2n]

= n(n)

= n²

Therefore, sum of first n term of natural numbers is n².