Write the sum of first n even natural numbers

Asked by admin @ 16/08/2021 in Math viewed by 281 People

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

Answered by admin @ 16/08/2021

Solution:

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Given & To Find:

The sum of first n even numbers,.

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The first even number = 2 (excluding 0)

d = 2,/ ( common difference between 2 even numbers)

We know that,

$S_n= \frac{n}{2}(2a + (n-1)d)$

Substituting the known values,

We get,

=> $S_n = \frac{n}{2}(2(2)+ (n-1)(2))$

=> $S_n= \frac{n}{2}(2(2 + (n-1)))$

=> $S_n = n (2 + n-1)$

=> ∴ $S_n = n (n+1) =n^2 +n$

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Hope it Helps!!

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