Find the sum of first n even natural numbers

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Write the sum of first n even natural numbers.

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Answer:

The sum of the first n even natural numbers is n [n + 1].

Step-by-step explanation:

Given :  

First n even natural numbers are 2,4 ,6 ,………., 2n  which forms an AP.

Here, a = 2, d = 4 - 2 = 2

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

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

Sn = n/2  [4  + 2n – 2]

Sn = n/2 × 2 [2  + n – 1]

Sn = n [n + 1]

Hence, the sum of the first n even natural numbers is n [n + 1].

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