Sequences

AQA GCSE Maths

8 ready-made resources for teaching Sequences, written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

Continue a sequence given the first few terms, and describe the term-to-term rule.
Recognise and use simple sequences: linear (arithmetic), square numbers, triangular numbers, and Fibonacci-type sequences.
Find and use the nth term rule for a linear (arithmetic) sequence.
Determine whether a given number is a term in a linear sequence.
Recognise and continue quadratic sequences and simple geometric progressions, including finding the common ratio of a geometric sequence, without necessarily deriving the algebraic rule.

Higher tier, in addition

Derive and use the nth term rule for a quadratic sequence.
Derive the nth term (general term) of a geometric sequence.
Derive a sequence's rule from a real-life or geometric growth context, rather than being given the rule.
Combine sequence reasoning with simultaneous equations to find unknowns that define a sequence.

Where students go wrong

Assuming the nth term's coefficient must match the common difference without correctly adjusting the constant term.
For quadratic sequences, using the first differences rather than the constant second differences to find the coefficient of n².
Confusing a term-to-term rule (how to find the next term) with a position-to-term rule (the nth term formula) when a question asks specifically for one.
Off-by-one errors when checking whether a number is a term in a sequence.

How it gets asked in the exam

"Find the nth term", "Is 200 a term in this sequence?", "Continue the sequence", "Find the next three terms".

Key vocabulary

Sequence, term, term-to-term rule, position-to-term rule (nth term), arithmetic sequence, geometric sequence, common difference, common ratio, quadratic sequence.

Assumed prior knowledge

Substituting values into algebraic expressions.
Solving linear equations.
Expanding brackets (for deriving an nth term from a visual pattern).
Basic ratio understanding (for geometric sequences).

How Speca scaffolds this topic

A difference-row visual (writing the sequence with colour-coded difference rows underneath) is the single most effective scaffold for deriving both linear and quadratic nth terms: use it consistently.
Provide a step-by-step template separating "find the pattern," "write the rule," and "test the rule" as three distinct, chunked stages.
Use physical/visual growth contexts (e.g. matchstick or tile patterns) before moving to purely numerical sequences, to dual-code the abstract rule against a concrete image.

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