0580/22 Feb/Mar 2023, Question 20: Quadratic and Cubic Sequences
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks
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The question, in short
Find the nth term formula for two given sequences: one starting −1, 0, 7, 26, 63, and one starting 24, 12, 6, 3, 1.5.
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Part (a) · 2 marks
Find the nth term of the sequence −1, 0, 7, 26, 63, …
- 1Add 1: 0, 1, 8, 27, 64 are the cubes 0³, 1³, 2³, 3³, 4³
- 2So the terms are (n − 1)³ − 1
- 3nth term = (n − 1)³ − 1
Answer(n − 1)³ − 1
Part (b) · 2 marks
Find the nth term of the sequence 24, 12, 6, 3, 1.5, …
- 1Each term is half the one before: first term 24, ratio 1/2
- 2nth term = 24 × (1/2)ⁿ⁻¹
Answer24 × (1/2)ⁿ⁻¹
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Also searched as: 0580/22/F/M/23 · 0580_m23_qp_22 · 0580 m23 22 · question 20.
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