A Level Maths: Sequences and Series Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Applied Sequences and Series (OCR)
- Applied Sequences and Series (Edexcel)
- Arithmetic Series (OCR)
- Arithmetic Series (Edexcel)
- General Binomial Expansion (OCR)
- General Binomial Expansion (Edexcel)
- Geometric Sequences (OCR)
- Geometric Sequences (Edexcel)
- Inductive Sequences and Sigma Notation (Edexcel)
- Mixed Sequences (OCR)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Exponentials and Logarithms — needed for finding n when given sums of geometric series
- Indices — needed for raising the common ratio to powers
- Binomial Expansion — connects to series ideas
A Level Maths sequences and series is a Year 2 Pure topic covering arithmetic and geometric sequences, sigma notation, and series convergence. You apply the standard formulas, recognise sequence types, and use them in real contexts like compound interest and financial modelling. The ideas here also support Numerical Methods and General Binomial Expansion.
You work with arithmetic sequences (constant common difference $d$), using $n$th term $a + (n-1)d$ and sum to $n$ terms $S_n = \tfrac{n}{2}(2a + (n-1)d)$. You work with geometric sequences (constant common ratio $r$), using $n$th term $ar^{n-1}$ and sum to $n$ terms $S_n = \frac{a(1 – r^n)}{1 – r}$. For geometric series with $|r| < 1$, you find the sum to infinity $S_\infty = \frac{a}{1 – r}$, useful for converging series. You handle inductive (recursive) sequences defined by relations like $x_{n+1} = f(x_n)$, identifying whether they are increasing, decreasing, or periodic. You use sigma notation $\sum$ for compact representation of sums. Applications include savings schemes, geometric decay (radioactive material, drug concentration), and problems mixing arithmetic and geometric series.
Sequences and series is part of the Pure Maths strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: the sum to infinity formula $\frac{a}{1-r}$ only works when $|r| < 1$ — for $|r| \ge 1$ the series diverges; the $n$th term formula uses $(n-1)$ in the exponent for geometric and $(n-1)$ coefficient for arithmetic — count from the FIRST term, not the zeroth; when finding the number of terms using logs (for geometric problems), be careful with inequality direction when $r$ is negative; and check whether the question asks for the $n$th term or the sum to $n$ terms — these are very different.