Question

Find the sum of first n even natural numbers. arithmetic progression

Answer 1

The first even numbers in AP are : 2,4,6,8....
therefore, a = 2
d = a2 - a1= 2
an = a + ( n -1 ) d
= 2 + ( n - 1) 2
= 2 + 2n - 2
an = 2n
Sn = ( a + an )
= 2 + 2n

​First odd numbers are : 1, 3, 5, 7, 9....
Therefore, a = 1
d = 2
an = a + ( n - 1 )d
= 1 + ( n - 1)2
= 1 + 2n -2
= 2n - 1
Sn = ( a + an )
= ( 1 + 2n -1)
= 2n
Hence, sum of (a) first 'n' even numbers natural numbers is 2 + 2n
sum of (b) first 'n' odd natural numbers is 2n.

Hope this will help you.... ✌