Algebra — Pearson GCSE Study Guide
Exam Board: Pearson | Level: GCSE
Sequences are the heartbeat of algebraic patterns, testing your ability to spot relationships and express them mathematically. Mastering term-to-term and position-to-term rules is essential for unlocking high marks in your GCSE Mathematics exam.
Overview
Sequences are a fundamental topic in GCSE Mathematics that bridge the gap between simple number patterns and complex algebra. A sequence is simply an ordered list of numbers, but the power lies in finding the rule that governs it. Examiners love sequences because they test multiple skills at once: pattern recognition, algebraic notation, and problem-solving. This topic connects heavily to linear graphs (where the common difference is the gradient) and functions.
In your exam, you can expect a range of question styles. Foundation tier often focuses on generating terms from a rule or identifying special sequences. Higher tier demands finding the nth term of quadratic sequences or proving whether a specific number belongs to a sequence. Let's break it all down.
Key Concepts
Concept 1: Term-to-Term Rules
A term-to-term rule tells you how to get from one number in the sequence to the very next number. You must know the previous term to find the next one.
Example: The sequence 3, 7, 11, 15... has a term-to-term rule of "add 4".
This is simple but limited. If an examiner asks for the 100th term, using a term-to-term rule would take forever! This is why we need position-to-term rules.
Concept 2: Position-to-Term Rules (The nth Term)
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