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4MA1/2FR Jan 2020, Question 9: The nth Term of a Linear Sequence

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

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The question, in short

Analyse a circle pattern sequence where patterns 1 to 4 contain 1, 4, 7 and 10 circles, then extend it, tabulate values, derive a formula and test a triangle rule.

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

Part (a) · 1 mark

Sketch the fifth pattern in the circle sequence.

  1. 1Pattern number 5 has 13 circles arranged in the same linear pattern as previous ones, increasing by 3 each time

AnswerPattern 5 drawn as Pattern 4 with 3 more circles added, giving 13 circles

Part (b) · 1 mark

Fill the missing circle counts for patterns 5 and 6 in the table.

  1. 1Pattern 1: 1 circle
  2. 2Each pattern increases by 3 circles
  3. 3Pattern 4: 10 circles
  4. 4Pattern 5: 10 + 3 = 13
  5. 5Pattern 6: 13 + 3 = 16

Answer13, 16

Part (c) · 1 mark

Calculate how many circles pattern 8 contains.

  1. 1Pattern 6: 16 circles
  2. 2Pattern 7: 16 + 3 = 19
  3. 3Pattern 8: 19 + 3 = 22

Answer22

Part (d) · 2 marks

Express C, the circle count for pattern P, as a formula involving P.

  1. 1The sequence increases by 3 each time, so C = 3P + k
  2. 2When P = 1, C = 1 → 3(1) + k = 1 → k = −2
  3. 3So C = 3P − 2

AnswerC = 3P − 2

Part (e) · 1 mark

Using the triangle rule (pattern number times 5, minus 4), decide whether 136 triangles can occur, justifying your conclusion.

  1. 1Number of triangles = 5 × P − 4
  2. 2Set 5P − 4 = 136
  3. 35P = 140
  4. 4P = 28
  5. 5So pattern 28 has exactly 136 triangles

AnswerYes, pattern 28 has 136 triangles

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