Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Triangles in a row use 3, 5, 7 sticks. How many sticks for 4 triangles?
Show worked solution
7 + 2 = 9.
2 Complete the table for squares in a row.
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7 + 3 = 10; 10 + 3 = 13.
3 A pattern has the rule 2n + 1. What is its 6th term?
Show worked solution
2 × 6 + 1 = 13.
Level 2 · Core
4 Triangles in a row use 3, 5, 7, 9 sticks. What is the rule for n triangles?
Show worked solution
Gap 2 → 2n. 2 × 1 = 2, first term 3 → + 1. 2n + 1. Check: 2 × 4 + 1 = 9 ✓.
5 The rule for squares in a row is 3n + 1. Give the 20th term and the 50th term.
Show worked solution
3 × 20 + 1 = 61; 3 × 50 + 1 = 151.
6 The rule 2n + 1 gives 41. What is n?
Show worked solution
2n = 40, so n = 20.
Level 3 · Challenge
7 Tiles around the edge of a square: 8, 12, 16, …1 The rule is 4n + 4.
2 The 10th pattern has 44 tiles.
3 Some pattern has exactly 50 tiles.
Which statements are correct?
2 The 10th pattern has 44 tiles.
3 Some pattern has exactly 50 tiles.
Which statements are correct?
Show worked solution
4n + 4 fits 8, 12, 16 (1 ✓). 4 × 10 + 4 = 44 (2 ✓). 4n + 4 = 50 gives n = 11.5, not whole (3 ✗). 1 and 2.
8 The border-tile rule is 4n + 4. Give the 5th term, and the pattern number that has 84 tiles.
Show worked solution
4 × 5 + 4 = 24. 4n = 80, so n = 20.
9 The rule 3n + 1 gives 151. What is n?
Show worked solution
3n = 150, so n = 50.