geometric progression

USAGE SUMMARY

"geometric progression" is a correct and commonly used phrase in written English.
It refers to a sequence of numbers in which each term is obtained by multiplying the previous term by a constant number. A possible example of using this phrase in a sentence could be: "The population growth in this city follows a geometric progression, with each generation being 1.5 times larger than the previous one."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

On the bottom, again with alpha positive, but now with its magnitude less than 1, we have a geometric progression that is exponentially or geometrically decaying.

Massachusetts Institute of Technology

But the cycles of appeasement usually get shorter with geometric progression.

The Guardian - Opinion

"But the two aren't cumulative; it won't result in geometric progression of disruption.

The New York Times

This is an example of what in mathematics is called a geometric progression.

The Guardian - Books

The scale of magnitudes comprises a geometric progression of brightness.

Encyclopedia Britannica

In this time-critical action scenario, concepts like "geometric progression" assume a certain urgency.

The New York Times - Tech

Comparison of Monte Carlo (EGS4-code) and Geometric Progression (G.P).

Radiation Physics and Chemistry

For close to two decades, James River, which went public in 1973, grew in almost geometric progression.

The New York Times

It is a geometric progression built into the brain, imposed on an irregular world.

The New York Times - Science

Four spreads of quarter-views follow, then eight of eighths, and so on, in a geometric progression to four-thousand-ninety-sixths.

The New Yorker

For some cosmologists, that means universes sprouting from one another in an endless geometric progression, like mushrooms upon mushrooms upon mushrooms, or baby universes hatched inside black holes.

The New York Times - Science

Expert writing Tips

Best practice

When using "geometric progression", ensure you're describing a sequence where each term is multiplied by a constant ratio to obtain the next. Avoid using it for sequences with additive relationships.

Common error

Don't mistake a "geometric progression" for an arithmetic one. Geometric progressions involve multiplication by a common ratio, while arithmetic progressions involve addition of a common difference. Understand the core mathematical difference to avoid misusing the term.

Linguistic Context

The phrase "geometric progression" functions as a noun phrase, typically serving as the subject or object of a sentence. It identifies a specific type of sequence in mathematics where each term is derived by multiplying the preceding term by a constant ratio. Ludwig examples illustrate its application in describing various phenomena.

Expression frequency: Very common

Frequent in

Science

53%

News & Media

31%

Academia

8%

Less common in

Encyclopedias

3%

Wiki

2%

Formal & Business

2%

Ludwig's WRAP-UP

The analysis reveals that "geometric progression" is a grammatically correct and very common noun phrase primarily used within scientific, news, and academic contexts. As Ludwig confirms, it refers to a sequence where each term is multiplied by a constant ratio. The term accurately models scenarios involving exponential growth or decay. When using "geometric progression", remember to differentiate it from "arithmetic progression" to avoid confusion. Ludwig's examples highlight its usage in modeling real-world phenomena and its significance in mathematical and scientific discourse.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

geometric sequence

Replaces "progression" with "sequence", a synonymous term in mathematics.

constant ratio sequence

Emphasizes the defining characteristic of a geometric progression: the constant ratio.

exponential growth

Focuses on the increasing aspect of a geometric progression where the common ratio is greater than 1.

exponential decay

Focuses on the decreasing aspect of a geometric progression where the common ratio is between 0 and 1.

geometric series

Refers to the sum of the terms in a geometric progression.

logarithmic progression

Relates to the inverse of exponential growth, reflecting a decreasing rate of increase.

exponential function

Connects the progression to its underlying function.

recursive sequence

Highlights the recursive nature of the sequence where each term depends on the previous one.

power series

A more general type of series that includes geometric series as a special case.

arithmetic progression

Presents a contrasting type of sequence where the difference between terms is constant, not the ratio.

FAQs

What is the difference between a geometric and an arithmetic progression?

A "geometric progression" involves multiplying each term by a constant ratio to get the next term. An "arithmetic progression" involves adding a constant difference to each term.

How is "geometric progression" used in real-world examples?

It's used to model phenomena with exponential growth or decay, such as population growth, compound interest, or radioactive decay. See Ludwig for example sentences from scientific and news sources.

What are some other terms that are similar to "geometric progression"?

Similar terms include "geometric sequence", "exponential growth" (when the ratio is greater than 1), and "exponential decay" (when the ratio is between 0 and 1).

How do you calculate the sum of a "geometric progression"?

The sum of a finite geometric progression can be calculated using a specific formula involving the first term, the common ratio, and the number of terms. An infinite "geometric progression" has a finite sum only if the absolute value of the common ratio is less than 1.