# Definition:Geometric Sequence/Also known as

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## Geometric Sequence: Also known as

The usual term for **geometric sequence** is **geometric progression**, and the abbreviation **G.P.** is often seen.

However, $\mathsf{Pr} \infty \mathsf{fWiki}$ prefers the term **sequence** as there is less likelihood of confusing it with **geometric series**, which the term **geometric progression** is also often used for.

Euclid used the term **continued proportion** throughout Book $\text{VIII}$ of *The Elements*, though never formally defining it.

In the words of Euclid:

*If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the numbers are the least of those which have the same ratio with them.*

(*The Elements*: Book $\text{VIII}$: Proposition $1$)

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**geometric progression** - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.2$: More about Numbers: Irrationals, Perfect Numbers and Mersenne Primes - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**geometric progression (geometric sequence)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**geometric progression (geometric sequence)**