Concept 12 of 19Foundation
Watch on YouTubeVideoPattern detective toolkit
When a pattern resists easy guessing, try these moves in order:
- Subtract neighbours. Constant → arithmetic.
- Divide neighbours. Constant → geometric.
- Compare to n² (1, 4, 9, 16…) or n³ (1, 8, 27…).
- Try second differences. If first diffs are arithmetic, the pattern is quadratic.
- Check if each term needs previous TWO (Fibonacci-style).
- Check for repeating cycles (period 2, 3, 4…).
Example
Sequence 2, 6, 12, 20, 30.
First diffs: 4, 6, 8, 10 — arithmetic. Pattern is quadratic. Check aₙ = n² + n → 2, 6, 12, 20, 30 ✓.
First diffs: 4, 6, 8, 10 — arithmetic. Pattern is quadratic. Check aₙ = n² + n → 2, 6, 12, 20, 30 ✓.
💡 Tip:Work simple to complex. Most olympiad patterns are arithmetic or quadratic.
▶Prefer a video? Open YouTube search for “how to find next number in a pattern class 6”↗🎯 Try it!
5 questions to check what you just read.
0 / 5
- Q1.Which method works on 3, 9, 27, 81?
- Q2.For 1, 4, 9, 16, 25, compare to:
- Q3.First differences of 2, 6, 12, 20, 30?
- Q4.A sequence with constant second differences is:
- Q5.Pattern 1, 1, 2, 3, 5, 8, 13 uses: