common ratio: meaning, definition, pronunciation and examples

Low
UK/ˈkɒmən ˈreɪʃiəʊ/US/ˈkɑːmən ˈreɪʃioʊ/

Technical / Academic

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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

strong
find the common ratiocalculate the common ratioa common ratio ofgeometric sequence
medium
positive common rationegative common ratioconstant common ratio
weak
termprogressionseriesmultiply by

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

multiplierprogression factor

Weak

factorr (as a variable)

Vocabulary

Antonyms of “common ratio”

common difference (arithmetic sequence counterpart)

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

Fill in the gap
If a geometric sequence begins with 5 and has a common ratio of 2, the third term is .
Multiple Choice

What is the common ratio in the sequence 81, 27, 9, 3?