0580/23 May/Jun 2023, Question 22: Quadratic and Cubic Sequences
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 5 marks
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The question, in short
Given the first four terms 2.75, 6, 11.25, 20 of a sequence with nth term (1/4)n³ + an² + bn, find the constants a and b.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1n = 1: 1/4 + a + b = 2.75, so a + b = 2.5
- 2n = 2: 2 + 4a + 2b = 6, so 2a + b = 2
- 3Subtract: (2a + b) − (a + b) = 2 − 2.5, so a = −0.5
- 4b = 2.5 − (−0.5) = 3
- 5a = −1/2, b = 3
Answera = −1/2, b = 3
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Also searched as: 0580/23/M/J/23 · 0580_s23_qp_23 · 0580 s23 23 · question 22.
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