Grade 11 · Mathematics
Arithmetic sequences
Why it matters
Common difference and nth term.
Last reviewed 2026-09-03 · accuracy standard
What is an arithmetic sequence?
Short answer
An arithmetic sequence is a list of numbers in which each term differs from the previous one by a constant amount called the common difference, d. Its nth term is given by tₙ = t₁ + (n − 1)d, where t₁ is the first term. For example, 3, 7, 11, 15, … has a common difference of 4.
Concept preview
What you will be able to do
- 01Recognise an arithmetic sequence and find its common difference
- 02Use the general term to find any term
- 03Find the first term and common difference from given terms, and solve word problems
Count by 5s: You have been doing this since primary school. A sequence is just an ordered list of numbers, and each number is called a term. What makes counting-by-5s special is that you add the same amount — 5 — to get from one term to the next. That single, simple idea is the whole of this lesson, dressed up in some new notation. We are not learning something alien; we are giving a precise name to a pattern you already feel.
School Plan
Arithmetic sequences
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Related topics
Frequently asked questions
- What is the common difference?
- The fixed amount added to each term to get the next; you find it by subtracting any term from the one after it.
- How is an arithmetic sequence different from a geometric one?
- Arithmetic sequences add a constant difference; geometric sequences multiply by a constant ratio.