Grade 11 · Mathematics
Geometric sequences
Why it matters
Common ratio and nth term.
Core20m readingPrerequisite: Arithmetic sequences
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.
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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.