0580/21 Oct/Nov 2021, Question 16: Pattern Sequences and Special Sequences
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 5 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Find the nth term formula for two sequences: 8, 15, 34, 71, 132, ... and 2/1, 3/4, 4/16, 5/64, 6/256, ...
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Find the nth term of the sequence 8, 15, 34, 71, 132, ...
- 1Differences 7, 19, 37, 61; 12, 18, 24; 6, 6: third differences 6, so cubic with n³
- 2Subtract n³ (1, 8, 27, 64, 125): 7, 7, 7, 7, 7
- 3nth term = n³ + 7
Answern³ + 7
Part (b) · 3 marks
Find the nth term of the sequence 2/1, 3/4, 4/16, 5/64, 6/256, ...
- 1Numerators 2, 3, 4, 5, 6 = n + 1
- 2Denominators 1, 4, 16, 64, 256 = 4⁰, 4¹, 4², … = 4ⁿ⁻¹
- 3nth term = (n + 1)/4ⁿ⁻¹
Answer(n + 1)/4ⁿ⁻¹
Stuck on a step? Read the free lesson: Pattern Sequences and Special Sequences
Practise more pattern sequences and special sequences questions
Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on pattern sequences and special sequences
Also searched as: 0580/21/O/N/21 · 0580_w21_qp_21 · 0580 w21 21 · question 16.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.