Number patterns
Strategy card
Model the sequence: arithmetic, geometric, polynomial, recursive or interleaved.
- Step 1: Check first and second differences and ratios.
- Step 2: Consider position-based rules (n², 2ⁿ, n(n+1)).
- Step 3: Consider recursive rules (each term from the previous one or two).
- Step 4: Verify the rule on all terms; one exception means it's wrong.
Tip: Write the term number above each term: rules often depend on position.
Worked example
Which number comes next?
8, 9, 13, 22, 38, 63, ?
- A: 99 (the answer)
- B: 105
- C: 94
- D: 81
- E: 82
Why: The differences are square numbers: +1, +4, +9, +16, … So the next number is 99.
Your turn
Your turn 1 of 3
Which number comes next?
2, 4, 3, 6, 5, 10, ?
Your turn 2 of 3
Which number comes next?
−1, 2, −4, 8, −16, 32, ?
Your turn 3 of 3
Which number comes next?
9, 10, 14, 23, 39, 64, ?
Keep practicing
Grown-ups: Discuss how compound interest makes a geometric sequence. Parent guide
Next lesson: Matrix rules