Question

Find the sum of first n even natural numbers.

Answer 1

The first n even natural numbers are 2, 4, 6, 8, 10, …., n.

Here, a = 2 and d =(4-2)= 2
Sum of n terms of an AP is given by

`s_n = n/2 [ 2a + (n-1) d]`

`= (n/2) xx [ 2xx2+ (n-1) xx 2 ] `

`=(n/2) xx [ 4 + 2n -2 ] = (n/2 ) xx (2n +2 ) = n(n+1)`

Hence, the required sum is n(n+1).