common ratio: meaning, definition, pronunciation and examples
LowTechnical / Academic
Quick answer
What does “common ratio” mean?
The constant factor by which each term in a geometric sequence is multiplied to obtain the next term.
Audio
Pronunciation
Definition
Meaning and Definition
The constant factor by which each term in a geometric sequence is multiplied to obtain the next term.
In a geometric progression, the fixed number that, when multiplied by any term, yields the following term.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or usage differences between BrE and AmE.
Connotations
Purely mathematical, neutral.
Frequency
Equally low-frequency and specialised in both dialects.
Grammar
How to Use “common ratio” in a Sentence
The common ratio [is/finds/calculates/equals] X.Vocabulary
Collocations
Usage
Meaning in Context
Business
Rare; only in financial modelling involving exponential growth/decay.
Academic
Primary context: mathematics, physics, and engineering education.
Everyday
Virtually never used.
Technical
Central term in discussions of geometric sequences/series, algorithms, and exponential processes.
Vocabulary
Synonyms of “common ratio”
Neutral
Weak
Vocabulary
Antonyms of “common ratio”
Watch out
Common Mistakes When Using “common ratio”
- Confusing it with 'common difference' of an arithmetic sequence.
- Thinking it's a general shared proportion.
- Incorrectly calculating it by addition/subtraction.
FAQ
Frequently Asked Questions
No, it can be any real number (including fractions, decimals, and negative numbers).
Divide any term (after the first) by the term immediately preceding it: r = a_n / a_{n-1}.
Technically yes, but it produces a trivial sequence (e.g., a, 0, 0, 0...).
In context, they are often synonymous. 'Growth factor' is used when the ratio is >1; 'decay factor' when 0<r<1.
The constant factor by which each term in a geometric sequence is multiplied to obtain the next term.
Common ratio is usually technical / academic in register.
Common ratio: in British English it is pronounced /ˈkɒmən ˈreɪʃiəʊ/, and in American English it is pronounced /ˈkɑːmən ˈreɪʃioʊ/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think 'Common Ratio = Constant RATIO you multiply by'. Both words start with 'R'.
Conceptual Metaphor
N/A (literal technical term).
Practice
Quiz
What is the common ratio in the sequence 81, 27, 9, 3?