Number patterns
Strategy card
Sequences can grow by steps, ratios, or changing differences.
- Step 1: Compute first differences; if constant, it's arithmetic.
- Step 2: If not, compute second differences or ratios.
- Step 3: Check for alternating sequences (odd and even positions).
- Step 4: Test the rule on every term before choosing.
Tip: Squares, cubes, and Fibonacci-like rules are common at this level.
Worked example
Which number comes next?
1, 3, 6, 10, 15, 21, ?
- A: 27
- B: 28 (the answer)
- C: 31
- D: 33
- E: 29
Why: Triangular numbers: add 1 more each step than the step before. So the next number is 28.
Your turn
Your turn 1 of 3
Which number comes next?
10, 13, 17, 22, 28, 35, ?
Your turn 2 of 3
Which number comes next?
2, 4, 7, 11, 16, 22, ?
Your turn 3 of 3
Which number comes next?
1, −2, 4, −8, 16, −32, ?
Keep practicing
Grown-ups: Look for patterns in savings plans or sports stats. Parent guide
Next lesson: Matrix rules