Write the sum of first n even natural numbers.

Question:

Write the sum of first n even natural numbers.

Solution:

In this problem, we need to find the sum of first n even natural numbers.

So, we know that the first odd natural number is 2. Also, all the odd terms will form an A.P. with the common difference of 2.

 

So here,

First term (a) = 2

Common difference (d) = 2

So, let us take the number of terms as n

Now, as we know,

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

So, for terms,

$S_{n}=\frac{n}{2}[2(2)+(n-1) 2]$

$=\frac{n}{2}[4+2 n-2]$

$=\frac{n}{2}(2+2 n)$

 

$=n(1+n)$

Therefore, the sum of first $n$ even natural numbers is $S_{n}=n(n+1)$.

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now