0580/42 Feb/Mar 2025, Question 13: Quadratic and Cubic Sequences
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 6 marks
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The question, in short
Using the given first five terms of sequences A, B and C in the table, write an expression for the nth term of each sequence.
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Solution · 6 marks
- 1A: differences 7, 19, 37, 61; third difference 6, so cubic: n³ + 1, 8, 27, 64, 125 → add 4: n³ + 4
- 2B: numerators 10, 9, 8, … = 11 − n; denominators 3, 4, 5, … = n + 2
- 3B: nth term (11 − n)/(n + 2)
- 4C: 4, 8, 16, … = 2², 2³, 2⁴, … so 2ⁿ⁺¹
AnswerA: n³ + 4, B: (11 − n)/(n + 2), C: 2ⁿ⁺¹
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