Sequences
A sequence is an ordered list of numbers that follow a rule from one term to the next.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
A sequence is an ordered list of numbers that follow a rule from one term to the next.
- Arithmetic sequences add a constant difference
- Geometric sequences multiply by a constant ratio
- The nth term rule gives any term directly
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Sequences?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Sequences. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Sequences in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Sequences gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Sequences in detail
A sequence is an ordered list of numbers that follows a rule, such as 3, 7, 11, 15, …. Each number is a term, and you can describe the pattern with a term-to-term rule (add 4 each time) or a position-to-term rule, the nth term, such as 4n − 1.
Spotting patterns in differences between terms helps classify the sequence as arithmetic, geometric, quadratic or something else. Sequences model regular growth, repeated payments, patterns in shapes and many real processes, and they lead to series and functions in later study.
How the interactive helps you understand Sequences
Click a card to flip it and reveal the answer, then move on to the next one.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Sequences.
Real-life uses and examples
- Explain Sequences to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Sequences in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Sequences by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Sequences without checking why they work.
- Forgetting units, signs or brackets when you apply Sequences.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Sequences
What is Sequences?
A sequence is an ordered list of numbers that follow a rule from one term to the next.
What are the most important points about Sequences?
The main points are: Arithmetic sequences add a constant difference; Geometric sequences multiply by a constant ratio; The nth term rule gives any term directly.
Why is Sequences useful?
Understanding Sequences gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Sequences?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Sequences?
Related topics in Mathematics include Fibonacci and Special Sequences, Expanding Brackets, Equations with Brackets and Fractions.