A Level Sequences and Series | 8 Lessons, Videos & Worksheets

This hub brings together a full set of A Level maths sequences and series lessons for Year 2 Pure: arithmetic and geometric progressions, sums, sigma notation, recurrence relations and modelling. It is written for teachers planning a coherent unit and for students searching for sequences and series A Level maths revision with video, worksheet and interactive lesson in one place.

Each lesson below follows the same pattern: a concise teaching video, a printable worksheet and an online lesson you can use in class or for independent study. Work through in order if you are meeting the topic for the first time, or jump to the lesson you need for targeted revision before past papers.

Published: April 2025  |  Last updated: 29 April 2026

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What you will cover in this sequences and series unit

• Arithmetic sequences: nth term, solving problems with unknown terms
• Arithmetic series: deriving and using the sum formula
• Geometric sequences: ratio, problem solving and non-linear equations
• Geometric series: finite sums and linking terms to the sum formula
• Sum to infinity for convergent geometric series
• Sigma notation: expanding sums, arithmetic and geometric forms, harder manipulation
• Recurrence relations: generating terms and linking to quadratics
• Modelling with sequences and series: contexts such as repeated events and structured change

Lesson 1: Introducing arithmetic sequences

Students learn to problem-solve with arithmetic sequences: finding the nth term, working with given terms and linking the common difference to the structure of the sequence.

As the lesson develops, they use arithmetic sequences to set up and solve simultaneous equations when more than one term is known, a common step-up in A Level exam questions.

Download worksheet (PDF) · Open online lesson

Lesson 2: Arithmetic series

Students derive and apply the formula for the sum of the first n terms of an arithmetic series, including recognising when a sum question is really asking about structure in the underlying sequence.

Later they use the sum formula to work backwards: finding the first term, common difference or number of terms when partial information is given.

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Lesson 3: Problem solving with geometric sequences

Students practise forming and solving equations with geometric sequences, using the common ratio to link terms and to interpret “which term first exceeds …” style prompts.

Progression focuses on non-linear equations that arise naturally from geometric structure, preparing for mixed exam questions that combine sequences with indices or surds.

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Lesson 4: Geometric series

Students derive and apply the formula for the sum of a finite geometric series, including careful treatment of the common ratio and the number of terms.

They then use the sum formula to find missing information: first term, common ratio or number of terms when a sum and partial term information are given.

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Lesson 5: Sum to infinity of a geometric series

Students learn the condition for convergence and how to derive and use the sum to infinity formula for a geometric series.

They practise working from sum-to-infinity information back to the first term and common ratio, including exam-style reasoning about validity (|r| < 1).

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Lesson 6: Sigma notation

Students evaluate sums written in sigma notation by expanding arithmetic and geometric forms and by spotting patterns that avoid unnecessary algebra.

Harder examples bring in algebraic manipulation and logarithmic identities where the unknown sits in the upper limit or inside the general term.

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Lesson 7: Recurrence relations

Students generate terms from a recurrence relation and interpret the rule as a bridge between consecutive terms.

They then use recurrence relations to form and solve quadratic equations, a standard A Level move when unknown constants appear in the rule.

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Lesson 8: Modelling with sequences and series

Students model repeated processes and structured change using arithmetic and geometric models, including contexts such as bouncing-ball style decay and regular payment structures.

The emphasis is on forming a sequence or series from the situation, solving the resulting equations and commenting on limitations of the model where appropriate.

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How to use this page for maximum revision value

• Watch the video once without pausing to get the full story of the method.
• Download the worksheet and attempt it before re-watching tricky steps.
• Use the online lesson for whole-class explanation or flipped homework.
• Mix lessons with past-paper questions that explicitly name sequences, series or sigma notation.

If you are comparing revision sites, this page is structured like a complete course map rather than a single clip: every subtopic in Edexcel-style Year 2 Pure sequences and series is represented with practice material to match.