0580/31 Oct/Nov 2025, Question 18: Quadratic and Cubic Sequences
Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 4 marks
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The question, in short
For a sequence with nth term n² − 4, find its first three terms, then work out the nth term rule for the sequence 5, 2, −1, −4.
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Part (a) · 2 marks
Substitute n = 1, 2 and 3 into n² − 4 to find the first three terms.
- 1n = 1: 1² − 4 = −3
- 2n = 2: 2² − 4 = 0
- 3n = 3: 3² − 4 = 5
- 4First 3 terms: −3, 0, 5
Answer−3, 0, 5
Part (b) · 2 marks
Find the nth term formula for the sequence 5, 2, −1, −4.
- 1Common difference = 2 − 5 = −3, so −3n
- 2n = 1: −3 × 1 + c = 5, so c = 8
- 3nth term = −3n + 8
Answer−3n + 8
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Also searched as: 0580/31/O/N/25 · 0580_w25_qp_31 · 0580 w25 31 · question 18.
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