A Level Maths · Pure · Year 12 and 13
Sequences and series covers the binomial expansion in Year 12, then arithmetic and geometric series, sigma notation and recurrence relations in Year 13. Many questions are set in context: savings, populations and repeated doses.
AS content is usually taught in Year 12. The full A Level adds the Year 13 content.
Find the coefficient of $x^3$ in the binomial expansion of $(2x - 1)^6$.
[M1] for identifying the specific term containing $x^3$: $\binom{6}{3} (2x)^3 (-1)^3$.
[A1] for evaluating the binomial coefficient $\binom{6}{3} = 20$.
[M1] for expanding the other terms correctly: $20 \times (8x^3) \times (-1)$.
[A1] for the final coefficient: $-160$.
Then practise: skills to practise · open sequences and series practice questions.
Every board examines the same A Level Maths content, set by the Department for Education. Only the paper it appears on and the section numbering differ.
| Board | Specification reference | Examined in |
|---|---|---|
| AQA 7357 | AQA section D | Paper 1, and Section A of Papers 2 and 3 |
| Edexcel 9MA0 | Edexcel topic Pure 4 | Paper 1 and Paper 2 |
| OCR A H240 | OCR reference 1.04 | Paper 1, and the pure sections of Papers 2 and 3 |
Three examples from the question bank. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.
Find the first three terms, in ascending powers of $x$, in the binomial expansion of $(5 - 3x)^4$.
Mark scheme: in the 48-hour free trial.
Given that $\binom{n}{2} = 45$, find the value of the positive integer $n$.
Mark scheme: in the 48-hour free trial.
The first three terms of an arithmetic sequence are $2k+1$, $4k-3$, and $5k+2$. Find the value of the constant $k$ and the 10th term of the sequence.
Mark scheme: in the 48-hour free trial.
Questions are original and written in the style of Edexcel 9MA0, and cover content that AQA and OCR examine too. They are not past-paper questions.
These skills sit in the Pure I unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Sequences and series can come up on these papers (from each board's paper structure). We haven't mapped individual questions yet, so open a recent paper and look for it.
| Board | Recent papers that can test it |
|---|---|
| Edexcel 9MA0 | Paper 1: June 2024, June 2023, June 2022 Paper 2: June 2024, June 2023, June 2022 |
| AQA 7357 | Paper 1: June 2023, June 2022, November 2021 Paper 2: June 2023, June 2022, November 2021 Paper 3: June 2023, June 2022, November 2021 |
| OCR H240 | Paper 1: June 2024, June 2023, June 2022 Paper 2: June 2024, June 2023, June 2022 Paper 3: June 2024, June 2023, June 2022 |
Papers are © the exam boards; each page links to the official question paper and mark scheme. All A Level Maths past papers →
Yes. Sequences and Series is part of the A Level Maths content that every board examines: AQA section D, Edexcel Pure 4, OCR 1.04. It is assessed in AQA Paper 1, and Section A of Papers 2 and 3; Edexcel Paper 1 and Paper 2; OCR A Paper 1, and the pure sections of Papers 2 and 3.
Both. The AS content, usually taught in Year 12, is: The binomial expansion of (a + bx)ⁿ for positive integer n, using nCr and factorial notation. The full A Level adds: The binomial expansion for any rational n and its range of validity; Arithmetic and geometric sequences and series, including sums to infinity; Sigma notation and recurrence relations; increasing, decreasing and periodic sequences; Modelling with sequences and series.
For positive integer n the expansion is finite and always valid. For negative or fractional n, (1 + bx)ⁿ is valid only when |bx| < 1. Exams often ask you to state this range.
Free, no sign-up. Then try every topic for 48 hours, no card needed.
Take the free diagnostic
A Level Math Revision