Question

The sum of first n odd natural numbers is
(a) 2n − 1
(b) 2n + 1
(c) $n^{2}$
(d) $n^{2}-1$

Answer 1

Answer:

The sum of the first n odd natural numbers is n².

Among the given options option (c)  n² is a correct answer.

Step-by-step explanation:

Given :  

First n Odd natural numbers are 1, 3 , 5, 7 ……….(2n - 1) which forms an AP.

Here, a = 1, d = 3 - 1 = 2

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

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

Sn = n/2  [2  + 2n – 2]

Sn = n/2 × 2 [1  + n – 1]

Sn = n [ n ]

Sn = n²

Hence, the sum of the first n odd natural numbers is n².

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Refer the attachment.