Lemmara logoLemmaraWorked solution

0580/23 Oct/Nov 2024, Question 13: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Find the nth term formula for two sequences: one arithmetic and one geometric, each worth 2 marks.

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 arithmetic sequence 21, 13, 5, −3, −11, …

  1. 1Common difference = 13 − 21 = −8, so the nth term is −8n + c
  2. 2Zero term = 21 + 8 = 29
  3. 3nth term = 29 − 8n

Answer29 − 8n

Part (b) · 2 marks

Find the nth term of the geometric sequence 2.5, 5, 10, 20, 40, …

  1. 1Each term is × 2 the one before, so the nth term is k × 2ⁿ
  2. 2First term: k × 2¹ = 2.5, so k = 1.25 = 5 × 2⁻²
  3. 3nth term = 5 × 2⁻² × 2ⁿ = 5 × 2ⁿ⁻²

Answer5 × 2ⁿ⁻²

Stuck on a step? Read the free lesson: The nth Term of a Linear Sequence

Practise more the nth term of a linear sequence 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 the nth term of a linear sequence

Also searched as: 0580/23/O/N/24 · 0580_w24_qp_23 · 0580 w24 23 · question 13.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.