IGCSE Math RevisionWorked example 1: nth term of a linear sequence
Find the nth term of 2, 9, 16, 23, …
Solution
- Common difference 7, so start with \(7n\): 7, 14, 21, 28.
- Each term is 5 less, so the nth term is \(7n-5\).
Answer: \(7n-5\)
Tip: Check: n = 1 gives 2.
Edexcel IGCSE Maths (4MA1) · Unit 3: Equations & Sequences
IGCSE Maths Sequences Questions and Answers
Sequences questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
- 3 worked examples
- 3 questions with mark schemes
- Higher tier · calculator allowed
- Free, no sign-in
What this topic covers
- Sequences 1: Term-to-Term & Linear nth Term: Term-to-term rules and finding the nth term of a linear sequence.
- Sequences 2: Arithmetic Progressions: nth-term rule for a linear (arithmetic) sequence.
- Sequences 3: Sum of an Arithmetic Series: Finding the sum of an arithmetic series with the Sₙ formula.
Sequences worked examples
Worked example 2: nth term of an arithmetic sequence
An arithmetic sequence has first term 7 and common difference 4. Find the 20th term.
Solution
- \(u_n=a+(n-1)d\).
- \(u_{20}=7+19\times4=83\).
Answer: 83
Tip: There are 19 steps from the 1st to the 20th term.
Worked example 3: Sum of an arithmetic series
Find the sum of the first 25 terms of \(5+8+11+\cdots\).
Solution
- \(a=5,\ d=3,\ n=25\).
- \(S_n=\tfrac{n}{2}(2a+(n-1)d)=\tfrac{25}{2}(10+72)\).
- \(=1025\).
Answer: 1025
Tip: Use n − 1, not n, with d.
Sequences exam-style questions
Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.
Question 1
Here are the first four terms of a sequence: 7, 11, 15, 19. (a) Write down the next two terms. (b) Write down the term-to-term rule.
Show the answer and mark scheme
- B1 23, 27
- B1 add 4
Answer: (a) 23, 27 (b) add 4
Question 2
The nth term of a sequence is \(3n+8\). Is 100 a term of the sequence? Give a reason for your answer.
Show the answer and mark scheme
- M1 3n + 8 = 100 or n = 92/3 oe, or terms 98 and 101 shown
- A1 No, with correct reason (n is not a whole number)
Answer: No: \(3n+8=100\) gives \(n=30\tfrac{2}{3}\), not an integer
Question 3
Sequence A has nth term \(4n+1\). Sequence B has nth term \(61-2n\). For one value of \(n\) the nth terms of the two sequences are equal. Find this value of \(n\) and the value of that term.
Show the answer and mark scheme
- M1 4n + 1 = 61 − 2n
- A1 n = 10
- A1 41
Answer: \(n=10\), term 41
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Revise sequences for the exam
- Unit 3 practice: Equations & Sequences in the student hub (more questions with mark schemes)
- IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
- Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
- IGCSE Maths 4MA1 examiner report summary: where students lose marks
Questions students ask
Which Edexcel IGCSE Maths papers test sequences?
Either Higher tier paper, 1H or 2H, can test sequences: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more sequences questions?
In the IGCSE student hub: Unit 3 (Equations & Sequences) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.