Quadratic sequence
- Look at first differences.
- Check second differences.
- Use the pattern to continue or find nth term.
Answer: 2, 5, 10, 17 has constant second difference 2
𝑥 Algebra
Quadratic sequences
Learn quadratic sequences with a GCSE-style explanation, help guide, worked example, practice question and flashcards.
Global XP
Level 10 / 100 XP
1. Explanation
Key idea
- Quadratic sequences is part of algebra and appears often in KS3–GCSE maths.
- Quadratic sequences have constant second differences.
- Use the worked model, help guide, interactive question and flashcards to practise quadratic sequences until the steps feel automatic.
Real-life examples
- Shopping, sport, travel, science, design and everyday decisions all use this skill.
2. Visual
Quadratic sequences learning map
Understand the key idea → follow the help guide → practise a question → check your method → build speed with flashcards.
3. Help guide
How to tackle Quadratic sequences
- Learn the rule: Quadratic sequences have constant second differences.
- Worked model: Look at first differences. Check second differences. Use the pattern to continue or find nth term.
- Try the interactive question without looking at the answer first.
- Use the flashcards to test the rule, the method and a common check.
4. Worked examples
Step-by-step working
5. Interactive questions
Try it yourself
What is the next term: 1, 4, 9, 16, ...?
6. Flashcards
Master quick recall
Flip each card, then choose whether you know it or need more practice.
0 mastered
FrontRule for Quadratic sequences
BackQuadratic sequences have constant second differences.
FrontExample answer: What is the next term: 1, 4, 9, 16, ...?
Back1², 2², 3², 4², so the next term is 5² = 25.
FrontCommon check for Quadratic sequences
BackCheck units/notation, compare with an estimate, and make sure the answer matches the question.
7. Finish
Complete this topic
When you have read the examples, tried the question and reviewed flashcards, claim your topic completion XP.