Sum of consecutive odd numbers

Recommended for You

Not sure where to start? These are the lessons and games we recommend most to students, parents and teachers on Basic-mathematics.com. Each lesson explains the topic in plain language, walks you through worked examples step by step, and ends with practice so you can check your understanding. Pick one below, or use the menu to find lessons on fractions, algebra, geometry, statistics and more.

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

Sum of consecutive even numbers