Sum of consecutive odd numbers

You can find the sum of consecutive odd numbers 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

1 + 3 + 5 = ?

Step 1

Count the number of terms: 3

Step 2

Square the number of terms: 3²

3² = 9

1 + 3 + 5 = 9

Indeed 1 + 3 + 5 = 4 + 5 = 9

Example #2

1 + 3 + 5 + 7 = ?

Step 1

Count the number of terms: 4

Step 2

Square the number of terms: 4²

4² = 16

1 + 3 + 5 + 7 = 16

Example #3

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = ?

Step 1

Count the number of terms: 9

Step 2

Square the number of terms: 9²

9² = 81

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81