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?
9, 16, 25, 36, 49, ?
- A: 63
- B: 57
- C: 54
- D: 64 (the answer)
- E: 70
Why: These are square numbers: 3×3, 4×4, and so on. So the next number is 64.
Your turn
Your turn 1 of 3
Which number comes next?
3, 8, 18, 38, 78, ?
Your turn 2 of 3
Which number comes next?
15, 18, 17, 20, 19, ?
Your turn 3 of 3
Which number comes next?
3, 23, 8, 22, 13, ?
Keep practicing
Grown-ups: Look for patterns in savings plans or sports stats. Parent guide
Next lesson: Matrix rules