0580/42 May/Jun 2021, Question 10: Pattern Sequences and Special Sequences
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks
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The question, in short
Complete the table for sequences A, B, C and D by filling in the missing 5th terms and nth term expressions.
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Solution · 9 marks
- 1A: cubes, 5th term = 5³ = 125, nth term = n³
- 2B: add 6 each time, 5th = 23 + 6 = 29, nth term = 6n − 1
- 3C: doubles each time from 0.25 = 2⁻², nth term = 2ⁿ⁻³ (5th term 4)
- 4D = B − C: 5 − 0.25 = 4.75, 11 − 0.5 = 10.5, …
- 5D: 5th term = 29 − 4 = 25, nth term = 6n − 1 − 2ⁿ⁻³
Answer| Sequence | 5th term | nth term | | A | 125 | n³ | | B | 29 | 6n − 1 | | C | 4 (given) | 2ⁿ⁻³ | | D | 25 | 6n − 1 − 2ⁿ⁻³ | or for D: 25.25 and −1/24n³ + 1/8n² + 17/3n − 1
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