How to see it
Make a table. Number of shapes, number of sticks. Find what changes each time, here +3. Then find a rule: three per square, plus one to start. 3n plus 1. A rule lets you jump straight to any term.
A worked example
20 squares: 3 times 20 plus 1, 61 matches. Check the rule against the pictures: n equals 3 gives 10.
The common mistake: doubling a non-proportional pattern
The trap is doubling. If 5 squares need 16, 10 squares must need 32? The rule says 31. The pattern does not double because the end stick is only there once.
Try one
5, 9, 13, 17, and so on. What is the 25th term?
- A100
- B101
- C97
- D105
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Right: B, 101
The rule is 4n plus 1.