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0580/41 Oct/Nov 2023, Question 6: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 11 marks

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The question, in short

Complete a table of missing terms and nth-term expressions for three sequences, then use two consecutive partial sums to find a specific term.

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

Part (a) · 10 marks

For sequences A, B and C, fill in the 5th term and the nth term expression for each.

  1. 1A: +4 each time, 5th term = 5 + 4 = 9; nth term = 4n − 11
  2. 2B: differences 6, 10, 14 (second difference 4) so next difference 18: 5th term = 37 + 18 = 55
  3. 3B: 2n² gives 2, 8, 18, 32; add 5: nth term = 2n² + 5
  4. 4C: numerators 2, 3, 4, 5 → n + 1; denominators 3³, 3⁴, 3⁵, 3⁶ → 3ⁿ⁺²
  5. 5C: 5th term = 6/3⁷ = 6/2187; nth term = (n + 1)/3ⁿ⁺²

Answer| Sequence | 5th term | nth term | | A | 9 | 4n − 11 | | B | 55 | 2n² + 5 | | C | 6/2187 | (n + 1)/3ⁿ⁺² |

Part (b) · 1 mark

Given the sums of the first 49 and first 50 terms are 7644 and 7975, find the 50th term.

  1. 150th term = 7975 − 7644 = 331

Answer331

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