Describe & continue number patterns
Theory
To continue a number pattern, find the rule that gets from one term to the next, then apply it again. Most patterns add or subtract a constant, but some multiply.
A number pattern is a list of numbers that follow a rule, such as \(5,\ 12,\ 19,\ 26,\ \dots\)
Each number is a term. The rule tells you how to get the next term.
Here each term is \(7\) more than the one before, so the rule is “add \(7\)”.
Common pattern rules
| Pattern | Rule |
|---|---|
| \(5,\ 12,\ 19,\ 26\) | add \(7\) |
| \(90,\ 78,\ 66\) | subtract \(12\) |
| \(48,\ 24,\ 12\) | halve |
How to continue a pattern
- Find the change from one term to the next.
- Check the same change works across the pattern.
- Apply the rule to get the next terms.
The rule is add \(7\).
\(26 + 7 = 33\), then \(33 + 7 = 40\).
| \(\text{next terms}\) | \(=\) | \(33,\ 40\) |
The rule is subtract \(12\).
\(66 - 12 = 54\), then \(54 - 12 = 42\).
| \(\text{next terms}\) | \(=\) | \(54,\ 42\) |
The rule is halve each time.
\(12 \div 2 = 6\), then \(6 \div 2 = 3\).
| \(\text{next terms}\) | \(=\) | \(6,\ 3\) |
\(12 + 9 = 21\), then \(21 + 9 = 30\).
He has $30 after week 3.
Common pitfalls
Frequently asked questions
How do I describe a pattern?
State what gets you from one term to the next, such as “add \(7\)” or “halve each time”.
How do I know if it adds or multiplies?
If the gaps are equal, the rule adds or subtracts. If the gaps grow or shrink, the rule multiplies or divides.
What is a term?
A term is one number in the pattern. The first term of \(5,\ 12,\ 19\) is \(5\).
How do I continue the pattern?
Apply the rule again to the last term. For “add \(7\)” from \(26\), the next term is \(33\).