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0580/33 Oct/Nov 2023, Question 7: Pattern Sequences and Special Sequences

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 8 marks

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The question, in short

Using a sequence of dot-and-line grid diagrams, complete a table, justify why 51 squares is impossible, and work with formulas for dots and lines.

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

Part (a) · 2 marks

Fill the missing entries for Diagram 4 in the table of small squares, dots and lines.

  1. 1Squares go up by 2: 6 + 2 = 8
  2. 2Dots go up by 3: 12 + 3 = 15
  3. 3Lines go up by 5: 17 + 5 = 22

Answer| Number of small squares | 8 | | Number of dots | 15 | | Number of lines | 22 |

Part (b) · 1 mark

Explain why no diagram in the sequence can contain 51 small squares.

  1. 1Number of small squares = 2n, which is always even
  2. 251 is an odd number

Answer51 is an odd number

Part (c) · 2 marks

Given dots = 3n + 3, determine which diagram number gives 249 dots.

  1. 13n + 3 = 249
  2. 23n = 246, n = 82
  3. 3Diagram 82

Answer82

Part (di) · 2 marks

Derive a formula in n giving the line count for Diagram n.

  1. 1Lines: 7, 12, 17, 22 — difference 5
  2. 2First term 7 = 5 × 1 + 2
  3. 3Lines = 5n + 2

Answer5n + 2

Part (dii) · 1 mark

Use your formula to calculate the line count for Diagram 41.

  1. 15 × 41 + 2 = 207

Answer207

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