geometric progression: meaning, definition, pronunciation and examples
C2Formal, Technical
Quick answer
What does “geometric progression” mean?
A sequence of numbers where each term after the first is found by multiplying the previous term by a constant value called the common ratio.
Audio
Pronunciation
Definition
Meaning and Definition
A sequence of numbers where each term after the first is found by multiplying the previous term by a constant value called the common ratio.
Any process, growth, or series that follows the pattern of multiplying by a fixed factor, often used metaphorically to describe rapid, exponential increases.
Dialectal Variation
British vs American Usage
Differences
No lexical or semantic differences. 'Geometric progression' is the standard term in both varieties. In some UK educational contexts, 'geometric series' may be used more frequently when discussing the sum of the terms.
Connotations
Identical technical connotations.
Frequency
Slightly more frequent in American academic texts according to corpus data, but the difference is marginal.
Grammar
How to Use “geometric progression” in a Sentence
[Subject] increases/grows in geometric progression.The numbers form/constitute a geometric progression.To calculate the sum of a geometric progression.Vocabulary
Collocations
Examples
Examples of “geometric progression” in a Sentence
verb
British English
- The values are not simply increasing; they are geometrically progressing.
American English
- The infection rate began to progress geometrically.
adverb
British English
- The company's value grew geometrically progressive.
American English
- The cells divided geometrically rapidly.
adjective
British English
- We observed a geometric-progression-like growth in the data.
American English
- The model assumes a geometric-progression increase.
Usage
Meaning in Context
Business
Used when describing compound growth, market expansion, or viral user acquisition, e.g., 'The app's user base grew in a geometric progression.'
Academic
Core term in mathematics, physics, economics, and biology for modeling exponential processes.
Everyday
Rarely used in casual conversation. May appear in discussions about savings interest, population growth, or pandemic spread.
Technical
Precise mathematical definition with formulas for the nth term (ar^(n-1)) and the sum of n terms.
Vocabulary
Synonyms of “geometric progression”
Strong
Neutral
Weak
Vocabulary
Antonyms of “geometric progression”
Watch out
Common Mistakes When Using “geometric progression”
- Confusing it with 'arithmetic progression' (adding a constant vs. multiplying by a constant).
- Using 'geometric progression' to describe any rapid increase, even if not truly multiplicative.
- Misspelling as 'geometrical progression'.
- Incorrectly stating the formula, e.g., confusing the common ratio with a difference.
FAQ
Frequently Asked Questions
In precise mathematics, a geometric progression is a discrete sequence (like 2, 4, 8, 16). 'Exponential growth' often refers to the continuous analogue described by an exponential function (like 2^x). In everyday language, they are used interchangeably to mean very rapid, multiplying growth.
The most common mistake is confusing it with an 'arithmetic progression' (linear growth by addition). Remember: Geometric multiplies, Arithmetic adds.
Yes. If the common ratio is between 0 and 1, the progression is decreasing (e.g., 16, 8, 4, 2). If it is negative, the terms alternate in sign.
It is crucial in finance (compound interest), computer science (algorithm complexity), biology (population growth of cells/bacteria), epidemiology (spread of disease), and physics (radioactive decay, though decay is a progression with a ratio less than 1).
A sequence of numbers where each term after the first is found by multiplying the previous term by a constant value called the common ratio.
Geometric progression is usually formal, technical in register.
Geometric progression: in British English it is pronounced /ˌdʒiː.əˌmet.rɪk prəˈɡreʃ.ən/, and in American English it is pronounced /ˌdʒiː.əˈmet.rɪk prəˈɡreʃ.ən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “To grow in geometric progression (metaphorical for rapid growth).”
Learning
Memory Aids
Mnemonic
Think of 'GEO' as 'Grow Exponentially by Multiplying'. A geometric progression multiplies, just as a geometry class might deal with shapes you can scale up by multiplication.
Conceptual Metaphor
GROWTH IS GEOMETRIC PROGRESSION (for rapid, multiplicative increase); SPREAD IS GEOMETRIC PROGRESSION (for viruses, information).
Practice
Quiz
What is the defining characteristic of a geometric progression?