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4024/21 Oct/Nov 2025, Question 10: The nth Term of a Linear Sequence

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 5 marks

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The question, in short

A dot pattern grows in a cross shape across four diagrams; students complete a table of dot counts, derive a formula for Pattern n, and work out which pattern number uses 1105 dots.

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

Part (a) · 1 mark

Fill in the missing dot totals for Patterns 4 and 5 in the given table.

  1. 1The number of dots goes up by 4 each time
  2. 213 + 4 = 17, 17 + 4 = 21

Answer17 and 21

Part (b) · 2 marks

Write a formula in terms of n giving the dot total for Pattern n.

  1. 1Common difference 4, so 4n + k
  2. 2n = 1: 4 + k = 5, k = 1
  3. 3Number of dots = 4n + 1

Answer4n + 1

Part (c) · 2 marks

Given that Pattern p needs 1105 dots, determine p.

  1. 14p + 1 = 1105
  2. 24p = 1104
  3. 3p = 276

Answer276

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