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4MA1/2F Jun 2018, Question 6: The nth Term of a Linear Sequence

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 7 marks

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The question, in short

Using a dot pattern that grows by four dots each time, complete the missing pattern, table entries, a specific term, a formula in n, and the largest pattern number under 90 dots.

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

Part (a) · 1 mark

Sketch the fourth pattern in the sequence, following the dot arrangement shown.

  1. 1Pattern 4 has 5 dots on each side forming an open square

Answer5 dots × 5 dots open square

Part (b) · 1 mark

Fill in the missing dot counts for pattern numbers 4 and 5 in the table.

  1. 1The number of dots goes up by 4 each time
  2. 2Pattern 4: 12 + 4 = 16, Pattern 5: 16 + 4 = 20
  3. 316, 20

Answer16, 20

Part (c) · 2 marks

Calculate how many dots appear in the pattern numbered 13.

  1. 1Number of dots = 4 × pattern number
  2. 24 × 13 = 52

Answer52

Part (d) · 1 mark

Write an expression using n that gives the dot count for pattern number n.

  1. 1Each pattern has 4 times the pattern number
  2. 2So for pattern n, number of dots = 4n

Answer4n

Part (e) · 2 marks

Determine the greatest k for which pattern number k contains fewer than 90 dots.

  1. 14k < 90
  2. 2k < 90 ÷ 4
  3. 3k < 22.5
  4. 4Largest whole number k is 22

Answer22

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