Home › GCSE › GCSE Maths › GCSE Percentages
GCSE Sequences Revision Guide
Master arithmetic, geometric, and quadratic sequences with our comprehensive guide designed for the AQA, Edexcel, and OCR specifications.
Foundation
Higher Tier
Exam Practice
Formulae
Topic Overview
Sequences are ordered lists of numbers that follow a specific pattern or rule. In your GCSE exams, you'll need to identify different types of sequences, find the "nth term" formula, and solve problems involving missing values in a pattern. Whether it's a simple linear growth or a complex quadratic relationship, mastering these rules is essential for higher-tier success.
Quick Navigation
Arithmetic
Geometric
Nth Term
Quadratic
Essential Formulae
an + b
a = common difference, b = zero-term
Linear nth term
Quadratic nth term
an² + bn + c
Requires second difference analysis
Lesson Modules
Arithmetic Sequences
Commonly known as linear sequences, these change by adding or subtracting the same amount each time.
Geometric Sequences
Patterns where each term is multiplied or divided by a fixed number (common ratio).
Nth Term Finder
The master key to sequences. Find the formula to predict any term in the series without counting.
Quadratic Sequences
Advanced patterns where the second difference is constant. Crucial for reaching Grade 8 or 9.
Core Subtopics
Structured lessons for every syllabus requirement.
Worked Example
Step-by-Step Walkthrough
THE QUESTION
Find the nth term of the sequence: 4, 7, 10, 13...
Method
- Find the common difference: 7 – 4 = 3. So the formula starts with 3n.
- Calculate the “zero-term” (one step back from the first term): 4 – 3 = 1.
- Combine them into the formula: 3n + 1.
Common Mistake
Confusing the first term (4) with the zero-term (1) and writing 3n + 4.
Final Answer
3n + 1
Revision Resources
Worksheet
Interactive Quiz
Exam Questions
Mark Scheme
Playlist
0:16
0:16
