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0580/43 May/Jun 2024, Question 2: Quadratic and Cubic Sequences

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 12 marks

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The question, in short

Work with three sequences: use nth-term formulas to find terms and a value of n, and complete a table of first terms and nth terms for sequences A, B and C.

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

Part (ai) · 1 mark

For the sequence with nth term 120 − n³, find the 4th term.

  1. 1120 − 4³ = 120 − 64 = 56

Answer56

Part (aii) · 2 marks

For the same sequence, find n when the nth term equals −1211.

  1. 1120 − n³ = −1211
  2. 2n³ = 1331
  3. 3n = 11

Answer11

Part (b) · 1 mark

For the sequence with nth term 3 × (0.2)ⁿ⁻¹, find the 5th term.

  1. 13 × 0.2⁴ = 3 × 0.0016
  2. 2= 0.0048

Answer0.0048 or 3/625

Part (c) · 8 marks

Complete the table for sequences A, B and C, giving the 5th term and nth term for each.

  1. 1A: difference −3, so 5th term −2 − 3 = −5 and nth term 10 − 3n
  2. 2B: numerators 1, 2, 3, 4 → n; denominators 4, 5, 6, 7 → n + 3; 5th term 5/8
  3. 3C: differences 2, 4, 6 → next 8, so 5th term 12 + 8 = 20
  4. 4C: second difference 2, so n² term; n² − n gives 0, 2, 6, 12 → nth term n² − n

AnswerA: 5th term −5, nth term 10 − 3n; B: 5th term 5/8, nth term n/(n + 3); C: 5th term 20, nth term n² − n

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Also searched as: 0580/43/M/J/24 · 0580_s24_qp_43 · 0580 s24 43 · question 2.
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