Lemmara logoLemmaraWorked solution

0580/42 May/Jun 2023, Question 6: Pattern Sequences and Special Sequences

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Work with sequences: generate terms from an nth-term formula, solve for a term's position, and derive nth-term expressions for two given sequences.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 2 marks

Using nth term n/(2n + 3), find the first three terms, giving each as a fraction.

  1. 1n = 1: 1/(2 + 3) = 1/5
  2. 2n = 2: 2/(4 + 3) = 2/7
  3. 3n = 3: 3/(6 + 3) = 3/9

Answer1/5, 2/7, 3/9

Part (aii) · 2 marks

Given the kth term equals 12/25, find the value of k.

  1. 1k/(2k + 3) = 12/25
  2. 225k = 12(2k + 3) = 24k + 36
  3. 3k = 36

Answer36

Part (bi) · 2 marks

Find the nth term of the sequence 6, 13, 32, 69, 130, …

  1. 1Compare with n³: 1, 8, 27, 64, 125
  2. 2Each term is 5 more: 6, 13, 32, 69, 130
  3. 3nth term = n³ + 5

Answern³ + 5

Part (bii) · 2 marks

Find the nth term of the sequence 100, 50, 25, 12.5, 6.25, …

  1. 1Each term is half the one before: first term 100, ratio 1/2
  2. 2nth term = 100 × (1/2)ⁿ⁻¹
  3. 3= 100 × 2¹⁻ⁿ

Answer100 × 2¹⁻ⁿ

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 Lemmara

More past-paper questions on pattern sequences and special sequences

Also searched as: 0580/42/M/J/23 · 0580_s23_qp_42 · 0580 s23 42 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.