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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