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Question

Sum of all the first 'n' terms of even natural number is


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Solution

Find the sum of the first 'n' terms of even natural numbers:

We know that first 'n'even natural numbers are 2,4,6,8,.........,2n.

Since any two consecutive terms of the sequence have the same difference, therefore this is an A.P.

We know that the sum of n terms of an AP =n22a+n-1d...........(1)

Where a is the first term of AP, and d is the common difference between any two consecutive terms of the AP.

Here a=2 and d=4-2=2

Substitute all the values in the equation (1). We get;

=n22×2+n-1×2=n24+2n-2=n22+2n=n2×21+n=nn+1

Therefore the sum of all the first 'n' terms of even natural number is nn+1.


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