Grade 11 · Mathematics
Geometric sequences
Why it matters
Common ratio and nth term.
Last reviewed 2026-09-03 · accuracy standard
What is a geometric sequence?
Short answer
A geometric sequence is a list of numbers in which each term is found by multiplying the previous term by a constant called the common ratio, r. Its nth term is tₙ = t₁ · r^(n − 1), where t₁ is the first term. For example, 2, 6, 18, 54, … has a common ratio of 3.
Concept preview
What you will be able to do
- 01Recognise a geometric sequence and find its common ratio
- 02Use the general term to find any term
- 03Model growth and decay, and find the common ratio from given terms
In an arithmetic sequence you added the same amount each time. A geometric sequence is the same idea with one word swapped: you multiply by the same amount each time. Think of doubling — — or halving — . That single change from adding to multiplying is the whole difference, but it makes the numbers behave very differently: geometric sequences can explode upward or shrink toward zero astonishingly fast.
School Plan
Geometric sequences
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Related topics
Frequently asked questions
- What is the common ratio?
- The fixed number each term is multiplied by to get the next; you find it by dividing any term by the one before it.
- Can a geometric sequence decrease?
- Yes. If the common ratio is between 0 and 1, the terms get smaller; a negative ratio makes them alternate in sign.