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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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