Worked example 1
3, 5, 9, 15, 23, ?
- Differences: 2, 4, 6, 8.
- Differences go up by 2, so the next is 10.
- 23 + 10 = 33.
Answer: 33
Brain Training · Mixed
Number sequence puzzles: find the rule
A sequence is a list of numbers that follows a rule. Finding the rule is a core reasoning skill used in maths, coding and aptitude tests.
- 1Learn it
- 2See it worked
- 3Try it online
- 4Print it
- 5Check your answer
Before you start
Who it's for and what to know first
Addition, subtraction and times tables.
Learn it
How it works
- Step 1: find the difference between neighbouring terms. If it is the same each time, add it.
- Step 2: if differences change, look at the differences of the differences, or check for multiplying.
- Step 3: check for special sequences: square numbers (1, 4, 9, 16), cube numbers, Fibonacci (each term is the sum of the two before).
- Step 4: some sequences alternate — two rules interleaved.
- Always test your rule on every term, not just the first two.
Try it online · print it · check it
Practice questions
Tips
Common mistakes
- Checking only the first two terms.
- Missing alternating patterns.
Last reviewed: 25 September 2026