Question

the sum of first n terms of odd natural numbers

Answer 1

First n Odd number form an arithmetic profession ;
1,3,5,7........n

a = 1
n = n
d = 2

Sn = n/2 (2a+(n-1)d)
= (n/2) [2×1 + (n-1)2]
= (n/2) (2+2n-2)
= (n/2) × (2n)
= n^2

Answer 2

The A.P of first n terms ---->
1 , 3,5,7,9..........n

Here first term , a = 1
Common difference , d = 3-1 = 2

S = n/2[ 2a + (n - 1)d]
S = n/2 [2 x 1 +( n - 1) 2]
S = n/2 [ 2 + 2n - 2]
S = n/2 x 2n
S = n xn
S = n²