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4024/22 May/Jun 2025, Question 15: The nth Term of a Linear Sequence

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Using bead patterns built as inverted triangles, fill in missing table values for pattern 5, derive formulas for white and total beads in pattern n, and find the largest pattern possible with 88 white beads.

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

Part (a) · 1 mark

Fill in the number of white beads and the total bead count for pattern 5 in the table.

  1. 1White beads go up by 2: 11 + 2 = 13
  2. 2Total beads go up by 4, 5, 6, then 7: 21 + 7 = 28

Answer| Number of white beads | 13 | | Total number of beads | 28 |

Part (bi) · 2 marks

Write an expression in terms of n for how many white beads pattern n contains.

  1. 1Common difference 2, so 2n + …
  2. 2n = 1: 2 × 1 + 3 = 5 ✓
  3. 3White beads = 2n + 3

Answer2n + 3

Part (bii) · 2 marks

Write an expression in terms of n for the total bead count of pattern n.

  1. 1Totals 6, 10, 15, 21: first differences 4, 5, 6; second differences 1, 1
  2. 2So 1/2 n² + bn + c; subtract 1/2 n²: 5.5, 8, 10.5, 13 (difference 2.5)
  3. 35.5 = 2.5 × 1 + 3, so bn + c = 5n/2 + 3
  4. 4Total = 1/2 n² + 5n/2 + 3

Answer1/2 n² + 5n/2 + 3

Part (c) · 2 marks

Given 88 white beads and unlimited black beads, determine the largest pattern number p that can be built.

  1. 12p + 3 = 88
  2. 22p = 85, p = 42.5
  3. 3Largest whole pattern: p = 42

Answer42

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Also searched as: 4024/22/M/J/25 · 4024_s25_qp_22 · 4024 s25 22 · question 15.
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