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4MA1/2F Jun 2019, Question 6: Pattern Sequences and Special Sequences

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 6 marks

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The question, in short

Stick patterns grow by adding squares; use the stick counts for patterns 1, 2 and 3 to continue the sequence and answer questions about pattern number and stick totals.

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

Part (a) · 1 mark

Draw Pattern number 4, continuing the arrangement of squares shown in the earlier patterns.

  1. 1Each pattern adds one column of 2 squares
  2. 2Pattern 4 is 4 squares wide and 2 squares high

AnswerA block of squares 4 wide and 2 high (8 squares), made from 22 sticks

Part (b) · 2 marks

Find the number of sticks needed to build Pattern number 7.

  1. 1Sticks: 7, 12, 17, … add 5 each time
  2. 2nth term = 5n + 2
  3. 35 × 7 + 2 = 37

Answer37

Part (c) · 2 marks

Determine which pattern number uses exactly 62 sticks.

  1. 15n + 2 = 62
  2. 25n = 60
  3. 3n = 12

Answer12

Part (d) · 1 mark

Decide whether a pattern with exactly 123 sticks can exist, giving a reason.

  1. 15n + 2 = 123
  2. 25n = 121
  3. 3n = 24.2, not a whole number
  4. 4So 123 is not in the sequence: Pedro is wrong

AnswerNo, because 5n + 2 = 123 gives n = 24.2, which is not a whole number (every term ends in 2 or 7)

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