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4MA1/1F Jan 2023, Question 3: Pattern Sequences and Special Sequences

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 4 marks

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The question, in short

A square pattern sequence is shown for patterns 1 to 3. Draw pattern 4, complete a table of square counts, find the count for pattern 8, and explain why 42 squares in pattern 15 is wrong.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Draw Pattern number 4 in the space provided, continuing the square arrangement shown.

  1. 1Pattern 1 has 1 square, Pattern 2 has 4 squares, Pattern 3 has 7 squares
  2. 2Each pattern has 3 more squares than the one before
  3. 3Pattern 4 has 7 + 3 = 10 squares
  4. 4Draw Pattern 3 with the next 3 squares added in the same way, so Pattern 4 has 10 squares in all

AnswerPattern number 3 continued in the same way with 3 more squares, giving 10 squares

Part (b) · 1 mark

Complete the table giving the number of squares for pattern numbers 4 and 5.

  1. 1Pattern 1: 1 square
  2. 2Pattern 2: 4 squares
  3. 3Pattern 3: 7 squares
  4. 4Each pattern increases by 3 squares
  5. 5Pattern 4: 7 + 3 = 10
  6. 6Pattern 5: 10 + 3 = 13

Answer10 and 13

Part (c) · 1 mark

Calculate how many squares are in Pattern number 8.

  1. 1The sequence increases by 3 each time
  2. 2Pattern 5 has 13 squares
  3. 3Pattern 6: 13 + 3 = 16
  4. 4Pattern 7: 16 + 3 = 19
  5. 5Pattern 8: 19 + 3 = 22

Answer22

Part (d) · 1 mark

Explain why Angus's claim of 42 squares in Pattern number 15 is incorrect.

  1. 1The number of squares follows the rule: number = 3 × pattern number − 2
  2. 2For pattern 15: 3 × 15 − 2 = 45 − 2 = 43
  3. 3So there should be 43 squares, not 42
  4. 4Angus is incorrect because 42 ≠ 43

AnswerPattern number 15 has 3 × 15 − 2 = 43 squares, not 42

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