Question

Write the sum of first n even natural numbers.

Answer 1

First n even Natural numbers are 2, 4, 6,……, 2n 

This forms an A.P where 

a= 2

l= 2n 

where l is last term of the A.P 

S_n = \(\frac{n}{2}\)(2a + (n–1) d) or \(\frac{n}{2}\)(a + l)

= \(\frac{n}{2}\)(2 + 2n)

= \(\frac{n}{2}\)[2(1 + n)]

= n (n + 1)