Sequences
Generate, recognise and generalise arithmetic, geometric, quadratic and recursive sequences.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Term-to-term and position-to-term rules
Exam cue: Inspect first and second differences or ratios, build a position-to-term rule and test it on several terms.
Concept 2
Arithmetic and quadratic sequences
Exam cue: Substitute known term numbers and generate the sequence to confirm both pattern and indexing.
Concept 3
Geometric and recursive sequences
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Foundation develops linear and simple recursive sequences. Higher extends to quadratic nth terms, geometric sequences and more formal generalisation and proof.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Giving a term-to-term description when an nth-term rule is required.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Arithmetic nth term
Common difference × n plus an adjustment.
Quadratic sequence signal
Constant second differences.
Geometric sequence signal
A constant multiplicative ratio.
Sequences: method
Inspect first and second differences or ratios, build a position-to-term rule and test it on several terms.
Sequences: check
Substitute known term numbers and generate the sequence to confirm both pattern and indexing.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Foundation · AO1 technique · Non-calculator — Find the next term of 7, 12, 17, 22, …
Shared F/H · AO1 technique · Non-calculator — Find the nth term of 4, 9, 14, 19, … evaluated at n=20.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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