Number patterns

Look at these numbers: 2, 5, 8, 11, 14… Can you guess what comes next? Each one is 3 more than the last. So the next number is 17. We just spotted a pattern.

What is this?

A number pattern is a sequence of numbers that follows a rule. The rule tells us how to get from one number to the next.

Common patterns:

• Add a fixed number each time: 5, 9, 13, 17, … (add 4). The rule: "add 4".
• Subtract a fixed number: 100, 90, 80, … (subtract 10).
• Multiply by a fixed number: 3, 6, 12, 24, 48, … (multiply by 2 each time).
• Squares: 1, 4, 9, 16, 25, … (1², 2², 3², …).
• Add a growing number: 1, 3, 6, 10, 15, … (add 2, then 3, then 4, …). These are the triangular numbers.

To find the next term, look at the difference between consecutive terms.

• For 2, 5, 8, 11, … the difference is 3 each time. Next = 11 + 3 = 14.
• For 1, 4, 9, 16, … the differences are 3, 5, 7. These themselves form a pattern! Next difference = 9. Next number = 16 + 9 = 25.

Number patterns also appear inside tables. The 9-times table: 9, 18, 27, 36, … Each digit in the ones place goes down by 1 (9, 8, 7, 6…), and the tens place goes up by 1 (0, 1, 2, 3…).

Spotting patterns is more important than memorising. Once you see the rule, you can extend the sequence forever.

Worked examples

Example 1. What comes next: 4, 8, 12, 16, ___?

• Difference is 4 each time.
• Next: 16 + 4 = 20.

Example 2. What comes next: 100, 91, 82, 73, ___?

• Subtract 9 each time.
• Next: 73 − 9 = 64.

Example 3. What comes next: 2, 4, 8, 16, ___?

• Multiply by 2 each time.
• Next: 16 × 2 = 32.

Try it

1. What comes next: 3, 7, 11, 15, ___?
2. What comes next: 50, 45, 40, 35, ___?
3. What comes next: 1, 3, 6, 10, ___?
4. What comes next: 5, 10, 20, 40, ___?
5. Make a pattern of your own with rule "add 7" starting from 4.

Hands-on

Hidden pattern. Write down the first 10 multiples of 9. Look at the digits' sum each time (9, 1+8=9, 2+7=9, …). What do you notice?

Pattern detective. Find a number pattern in the world , house numbers on one side of a road, page numbers in a book chapter, dates of every Monday in a calendar. Describe the rule.