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0580/12 May/Jun 2026, Question 21: Pattern Sequences and Special Sequences

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 6 marks

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The question, in short

Given the first four diagrams of a sequence built from grey and white squares, draw the fifth diagram, fill in a table for diagram 4 and diagram n, and explain why 120 total squares is impossible.

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

Part (a) · 1 mark

On the blank grid, draw the fifth diagram in the sequence.

  1. 1Draw a row of 5 grey squares
  2. 2Above the grey squares from the left, draw white columns of 4, 3, 2, 1
  3. 3Below, draw white columns of 4, 3, 2, 1 in the same way

AnswerHorizontal row of 5 grey squares, with white columns of 4, 3, 2, 1 squares above and 4, 3, 2, 1 squares below the first four grey squares

Part (b) · 4 marks

Fill the missing entries for diagram 4 and for diagram n in the grey, white and total square counts.

  1. 1Diagram 4: 4 grey squares, 2 × (3 + 2 + 1) = 12 white squares, total 16
  2. 2Grey squares go 1, 2, 3, 4 so n
  3. 3Totals 1, 4, 9, 16 are square numbers so n²
  4. 4Check: n + n(n − 1) = n²

AnswerDiagram 4: 4, 12, 16; diagram n: grey n, total n²

Part (c) · 1 mark

Finish the sentence explaining why no diagram in the sequence has 120 squares in total.

  1. 1Total number of squares is n²
  2. 2120 is between 10² = 100 and 11² = 121
  3. 3So 120 is not a square number

Answer120 is not a square number

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Also searched as: 0580/12/M/J/26 · 0580_s26_qp_12 · 0580 s26 12 · question 21.
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