Lemmara logoLemmaraWorked solution

0580/31 May/Jun 2026, Question 25: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Sequence starts 3, 7, 11, 15. Find its nth term, show 603 belongs to it, and for a different sequence with nth term n² − 6 find the first three terms.

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

Part (ai) · 2 marks

Find the nth term of the sequence whose first four terms are 3, 7, 11, 15.

  1. 1Common difference = 4, so 4n
  2. 2When n = 1, 4n = 4 and the term is 3, so subtract 1
  3. 3nth term = 4n − 1

Answer4n − 1

Part (aii) · 2 marks

Show that 603 is a term of the sequence with first terms 3, 7, 11, 15.

  1. 14n − 1 = 603
  2. 24n = 604
  3. 3n = 151, which is a whole number, so 603 is the 151st term

Answer4n − 1 = 603 gives n = 151, a whole number, so 603 is a term

Part (b) · 2 marks

For the sequence with nth term n² − 6, find the first three terms.

  1. 1n = 1: 1² − 6 = −5
  2. 2n = 2: 2² − 6 = −2
  3. 3n = 3: 3² − 6 = 3

Answer−5, −2, 3

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: 0580/31/M/J/26 · 0580_s26_qp_31 · 0580 s26 31 · question 25.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.