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4024/22 Oct/Nov 2025, Question 13: Pattern Sequences and Special Sequences

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

Work with two sequences: one starting 3, 8, 13, 18, 23, and another with terms given as fractions; find a missing term, a general formula, and a specific fraction term.

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Part (ai) · 1 mark

State the value that comes after 23 in the sequence 3, 8, 13, 18, 23.

  1. 1The terms go up by 5: 23 + 5 = 28

Answer28

Part (aii) · 2 marks

Give a formula in terms of n that produces the sequence 3, 8, 13, 18, 23.

  1. 1Common difference 5, so 5n + k
  2. 2n = 1: 5 + k = 3, k = −2
  3. 3nth term = 5n − 2

Answer5n − 2

Part (b) · 3 marks

For the fraction sequence with T₁ = 3/4, T₂ = 8/9, T₃ = 13/16, T₄ = 18/25, T₅ = 23/36, determine T₂₅.

  1. 1Numerators: 5n − 2; denominators 4, 9, 16, 25, 36 = (n + 1)²
  2. 2Tₙ = (5n − 2)/(n + 1)²
  3. 3T₂₅ = (5 × 25 − 2)/26² = 123/676

Answer123/676

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Also searched as: 4024/22/O/N/25 · 4024_w25_qp_22 · 4024 w25 22 · question 13.
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