Find the sum of first n even natural numbers.

Question

Philoid · Accepted Answer

First n even natural numbers are 2, 4, 6,…, 2n.

To find: sum of these n even natural numbers.

The even natural numbers forms an AP with first term 2 and common difference 2.

Now, Sum of first n terms of an AP is given by:

S_n = [2a + (n - 1)d]

where a is the first term and d is the common difference.

∴ Sum of first n natural numbers is given by:

S_n = [2(2) + (n - 1)(2)]

= [4 + 2n - 2]

= [2n + 2]

= n (n + 1)

∴ Sum of first n even natural numbers is n(n + 1).