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, 27, 64, 125, 216, 343, ?
- A: 545
- B: 538
- C: 479
- D: 512 (the answer)
- E: 500
Why: These are cube numbers (n × n × n). So the next number is 512.
Your turn
Your turn 1 of 3
Which number comes next?
1, 3, 7, 15, 31, 63, ?
Your turn 2 of 3
Which number comes next?
8, 30, 14, 26, 20, 22, ?
Your turn 3 of 3
Which number comes next?
6, 10, 15, 21, 28, 36, ?
Keep practicing
Grown-ups: Discuss how compound interest makes a geometric sequence. Parent guide
Next lesson: Matrix rules