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?
3, 5, 7, 11, 13, 17, ?
- A: 19 (the answer)
- B: 20
- C: 18
- D: 16
- E: 21
Why: These are prime numbers in order (numbers with exactly two factors). So the next number is 19.
Your turn
Your turn 1 of 3
Which number comes next?
7, 11, 13, 17, 19, 23, ?
Your turn 2 of 3
Which number comes next?
3, 5, 7, 11, 13, 17, ?
Your turn 3 of 3
Which number comes next?
2, −4, 8, −16, 32, −64, ?
Keep practicing
Grown-ups: Discuss how compound interest makes a geometric sequence. Parent guide
Next lesson: Matrix rules