Q. 184.4( 7 Votes )

Find the sum of first n even natural numbers.

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:


Sn = [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:


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


= [4 + 2n - 2]


= [2n + 2]


= n (n + 1)


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


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