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Number patterns

Strategy card

Model the sequence: arithmetic, geometric, polynomial, recursive or interleaved.

  1. Step 1: Check first and second differences and ratios.
  2. Step 2: Consider position-based rules (n², 2ⁿ, n(n+1)).
  3. Step 3: Consider recursive rules (each term from the previous one or two).
  4. 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