0580/42 Oct/Nov 2025, Question 10: The nth Term of a Linear Sequence
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 4 marks
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The question, in short
Find the nth term formula for two sequences: 17, 9, 1, −7, −15, … and 3, 12, 27, 48, 75, …
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Part (a) · 2 marks
Find the nth term of the linear sequence 17, 9, 1, −7, −15, …
- 1Differences: 9 − 17 = −8, so the nth term is −8n + k
- 2First term: 17 = −8 × 1 + k, so k = 25
- 3nth term = 25 − 8n
Answer25 − 8n
Part (b) · 2 marks
Find the nth term of the sequence 3, 12, 27, 48, 75, …
- 1First differences: 9, 15, 21, 27
- 2Second difference = 6, so the sequence is quadratic with 6 ÷ 2 = 3n²
- 33n² gives 3, 12, 27, 48, 75, which matches
- 4nth term = 3n²
Answer3n²
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