Topics › Algebra › Q144
Pattern · matchsticks
P6 · Algebra · PSLE Maths
Question
Ali uses matchsticks to make a row of equal squares. Figure 1 has 1 square. Figure 2 has 2 squares sharing one side. Figure 3 has 3 squares sharing sides, and so on. How many matchsticks are needed for Figure n? How many matchsticks are needed for Figure 20?
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Hint
Count Figure 1 first, then see how many matchsticks are added when one more square is joined.
Show the answer and step-by-step explanation
Answer: Figure n 3n+1 matchsticks; Figure 20 61 matchsticks
- Start with Figure 1 — Figure 1 is 1 square. One square needs 4 matchsticks.
- Add Figure 2 — When the second square is joined, it shares one side with the first square. So only 3 new matchsticks are added.
- Add one more — The third square also shares one side. So again, only 3 matchsticks are added.
- Find the rule — Figure 1 has 4 matchsticks. After that, each extra square adds 3 matchsticks. In Figure n, the increase happens n − 1 times.
- Write the expression — Simplify the expression: 4 + 3(n − 1) = 3n + 1. So Figure n needs 3n + 1 matchsticks.
- Find Figure 20 — Substitute n = 20: 3 × 20 + 1 = 61. Check: Figure 1 has 4 matchsticks, then there are 19 increases of 3 each. 4 + 19 × 3 = 61. 📌 Key idea: find the first term and the increase each time; nth term = first term + increase × (n − 1).
Method: For pattern questions, find the starting number and the increase each time. nth term = first term + increase × (n − 1).
Practice: 3 similar questions
- Mei Ling uses matchsticks to make a row of squares. Figure 1 has 1 square, and each extra square shares one side. How many matchsticks are needed for Figure n? How many are needed for Figure 12?
Answer
0 matchsticks, 37 matchsticks — Figure 1 needs 4 matchsticks. Each extra square adds only 3 new matchsticks. Figure n: 4 + 3(n − 1) = 3n + 1. Figure 12: 3 × 12 + 1 = 37 matchsticks.
- Raju uses toothpicks to make a row of equal triangles. Figure 1 has 1 triangle. After that, each extra triangle shares one side with the previous triangle. How many toothpicks are needed for Figure n? How many are needed for Figure 25?
Answer
0 toothpicks, 51 toothpicks — Figure 1 needs 3 toothpicks. Each extra triangle adds 2 toothpicks. Figure n: 3 + 2(n − 1) = 2n + 1. Figure 25: 2 × 25 + 1 = 51 toothpicks.
- Siti uses matchsticks to make a grid of squares with 2 rows and n columns. Figure 1 is a 2-by-1 grid with 2 squares. Figure 2 is a 2-by-2 grid, and so on. How many matchsticks are needed for Figure n? How many are needed for Figure 10?
Answer
0 matchsticks, 52 matchsticks — Figure 1 is a 2-by-1 grid and needs 7 matchsticks. Each extra column adds 2 vertical matchsticks and 3 horizontal matchsticks, making 5 in all. Figure n: 7 + 5(n − 1) = 5n + 2. Figure 10: 5 × 10 + 2 = 52 matchsticks.
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