GCSE MATHS PRACTICE
GCSE Sequences Questions
An arithmetic sequence has a constant difference between consecutive terms. A term-to-term rule tells you how to get the next term; an nth-term rule gives a term directly from its position n, starting at n = 1. For a linear rule an + b, a is the common difference. Use the first term to find b. This page focuses on arithmetic sequences.
Updated 11 October 2026
Worked example
Find the nth term of 7, 11, 15, 19, …
- The common difference is 4, so start with 4n.
- The sequence 4n gives 4, 8, 12, 16, … . Each required term is 3 greater, so the rule is 4n + 3.
- Check n = 1 and n = 4: 4 × 1 + 3 = 7 and 4 × 4 + 3 = 19.
Answer: 4n + 3
Practice questions
- 1
Write the next two terms of 6, 10, 14, 18, … and state the common difference.
- 2
Fill the two gaps in this arithmetic sequence: 31, __, 21, __, 11.
- 3
Find the nth term of 5, 12, 19, 26, … and use it to find the 20th term.
- 4
A sequence has nth term 6n + 1, starting at n = 1. Is 100 a term of this sequence?
Show answers
- 1. 22, 26; common difference 4
- 2. 26, 16
- 3. 7n − 2; 20th term 138
- 4. No (it would require n = 16.5).
Common mistakes
- Giving only the difference — Add 4 is a term-to-term rule; it is not an nth-term expression.
- Starting the position at zero — Here the first term has n = 1.
- Accepting a fractional position — Membership requires a positive whole-number position n.