Topics / Maths
Number sequences
Number sequences follow a rule: adding the same amount, multiplying, or a pattern of changing differences. The skill is finding the rule and then applying it.
What is tested
- Arithmetic sequences (add or subtract a constant)
- Geometric sequences (multiply by a constant)
- Square, cube and Fibonacci-style patterns
Worked example
What comes next in 4, 10, 16, 22, ...?
- Differences: 10 − 4 = 6, 16 − 10 = 6, 22 − 16 = 6.
- The rule is add 6.
- Next term: 22 + 6 = 28.
Answer: 28
Exam-day checklist
- Write the differences between neighbouring terms.
- If differences are not constant, test multiplying or look at the differences of the differences.
- Test your rule on every term.
- Check for square or triangular numbers.
Common mistakes
- Testing the rule on only the first two terms.
- Confusing adding with multiplying.
- Missing a sequence that alternates two rules.
Try it yourself
1. Find the next term: 2, 6, 18, 54, ...
Show answer
162
Each term is multiplied by 3: 54 × 3 = 162.
2. Find the next term: 1, 4, 9, 16, ...
Show answer
25
These are square numbers: 5 × 5 = 25.
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