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0580/32 Oct/Nov 2024, Question 3: Linear Sequences and Common Difference

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 8 marks

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The question, in short

Work with shape and number patterns: extend a square-and-triangle shape sequence, continue a decreasing sequence, and find nth terms for two sequences.

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

Part (ai) · 1 mark

On the grid, sketch the third shape in the square-and-triangle pattern.

  1. 1Shape 3: 3 squares side by side
  2. 2One triangle on each outer side: 3 on top, 3 on bottom, 1 at each end (8 triangles)

AnswerCorrect shape

Part (aii) · 1 mark

Work out how many triangles the fifth shape contains.

  1. 1Triangles = 2n + 2 (4, 6, 8, …)
  2. 2Shape 5: 2 × 5 + 2 = 12

Answer12

Part (bi) · 2 marks

Continue 32, 25, 18, 11 by writing the following two terms.

  1. 111 − 7 = 4
  2. 24 − 7 = −3

Answer4, −3

Part (bii) · 1 mark

State the rule that moves from each term to the next in 32, 25, 18, 11.

  1. 1Each term is 7 less than the one before: subtract 7

AnswerSubtract 7

Part (ci) · 2 marks

For 5, 8, 11, 14, ..., give an expression for the nth term.

  1. 1Common difference 3, so 3n + c
  2. 2First term: 3 × 1 + c = 5, c = 2
  3. 3nth term = 3n + 2

Answer3n + 2

Part (cii) · 1 mark

For 1, 8, 27, 64, ..., give an expression for the nth term.

  1. 11 = 1³, 8 = 2³, 27 = 3³, 64 = 4³
  2. 2nth term = n³

Answern³

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Also searched as: 0580/32/O/N/24 · 0580_w24_qp_32 · 0580 w24 32 · question 3.
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