# Sum of consecutive even numbers

The sum of consecutive even numbers can be found in 4 seconds or less using this trick. What is the trick? Take a look at the three examples below showing how to do this in 2 steps.

Example #1

2 + 4 + 6 + 8 = ?

Step 1

Count the number of terms: 4

Step 2

The product of (number of terms) times (number of terms + 1) is the answer

Number of terms = 4

Number of terms + 1 = 5

4 × 5 = 20

2 + 4 + 6 + 8 = 20

Indeed 2 + 4 + 6 + 8 = 6 + 6 + 8 = 12 + 8 = 20

Example #2

2 + 4 + 6 + 8 + 10 + 12 + 14 = ?

Step 1

Count the number of terms: 7

Step 2

The product of (number of terms) times (number of terms + 1) is the answer

Number of terms = 7

Number of terms + 1 = 8

7 × 8 = 56

2 + 4 + 6 + 8 + 10 + 12 + 14 = 56

Example #3

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = ?

Step 1

Count the number of terms: 10

Step 2

The product of (number of terms) times (number of terms + 1) is the answer

Number of terms = 10

Number of terms + 1 = 11

10 × 11 = 110

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110

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