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?
5, 9, 14, 23, 37, ?
- A: 60 (the answer)
- B: 65
- C: 64
- D: 71
- E: 72
Why: Each number is the sum of the two before it. So the next number is 60.
Your turn
Your turn 1 of 3
Which number comes next?
4, 8, 16, 32, 64, ?
Your turn 2 of 3
Which number comes next?
4, 9, 16, 25, 36, ?
Your turn 3 of 3
Which number comes next?
4, 9, 16, 25, 36, ?
Keep practicing
Grown-ups: Look for patterns in savings plans or sports stats. Parent guide
Next lesson: Matrix rules