Sum of Even Numbers Formula

About Sum of Even Numbers Formula

Sum of even numbers is number sequence beginning with 2 and ending with infinity. Even numbers, as we know, are those that are divisible by two, such as 2,4,6,8,10, and so on. We must apply the sum of arithmetic progression formula or the sum of natural numbers formula to find the sum of even numbers formula.

What do you mean by Sum of Even Numbers Formula?

The formula for finding the arithmetic progression is used to determine the sum of even numbers formula. The sum of even numbers can carry on forever. The sum of natural numbers formula can also be used to assess the sum of even numbers formula.

Formula for 2 + 4+ 6+ 8+ 10 +...... 2n must be found. Even numbers add up to 2(1 + 2+ 3+.....n). 2(sum of n natural numbers) is equal to 2[n(n+1)]/2 = n(n+1)

The formula of Sum of Even Numbers

S = n(n+1) , where n is number of terms in series

Sum of First Ten Even Numbers

Let us look at a table for sum of even numbers from 1 to 10, are consecutive: Sn = 2+4+6+8+10+... 10 terms

nth term in the AP Sum of Even Numbers Sn = n(n + 1) verification of the sum
1 1(1 + 1) = 1 x 2 = 2 2
2 2(2 + 1) = 2 x 3 = 6 2 + 4 = 6
3 3(3 + 1) = 3 x 4 = 12 2 + 4 + 6 = 12
4 4(4 + 1) = 4 x 5 = 20 2 + 4 + 6 + 8 = 20
5 5(5 + 1) = 5 x 6 = 30 2 + 4 + 6 + 8 + 10 = 30
6 6(6 + 1) = 6 x 7 = 42 2 + 4 + 6 + 8 + 10 + 12 = 42
7 7(7 + 1) = 7 x 8 = 56 2 + 4 + 6 + 8 + 10 + 12 + 14 = 56
8 8(8 + 1) = 8 x 9 = 72 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 = 72
9 9(9 + 1) = 9 x 10 = 90 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90
10 10(10 + 1) = 10 x 11 = 110 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110

Example: What is the sum of the first 20 even numbers?

Sol: Natural numbers present among first 20 numbers are. n = 20.

Now, let us find the sum of the first 20 even numbers

Sn= n(n+1)

Sn= 20(20+1)

Sn= 420

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Sum of Even Numbers Formula

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