# Definition of *arithmetic progression* in English:

## arithmetic progression

Syllabification: ar·ith·met·ic pro·gres·sionPronunciation: /ˌeriTHˌmedik prəˈɡreSH(ə)n
/

(also arithmetic series)

### noun

1A sequence of numbers in which each differs from the preceding by a constant quantity (e.g., 3, 6, 9, 12, etc.; 9, 7, 5, 3, etc.).

More example sentences

- Dutch mathematician Bartel L. van der Waerden was for one of the first to identify such a pattern among integers - one that involves arithmetic progressions in sets of numbers.
- The following year he published An elementary proof of the prime number theorem for arithmetic progressions.
- In one step toward elucidating certain primal mysteries, two mathematicians have now apparently proved that the population of primes contains an infinite collection of arithmetic progressions.

1.1The relationship between numbers in an arithmetic progression:

*the numbers are in arithmetic progression*More example sentences

- Dubner, Zimmermann, and Forbes are now looking for help to find a sequence of nine consecutive primes in arithmetic progression.
- In this instance, the integers 6, 9, 1 constitute a three-term rainbow arithmetic progression with a common difference of 3.
- A theorem of Peter Gustav Lejeune Dirichlet on primes in arithmetic progression guarantees that all the other notes are heard infinitely often when one plays all the primes.

## Definition of **arithmetic progression** in:

- The British & World English dictionary

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Pronunciation: ˈjôntē

adjective

having a lively, cheerful, and self-confident manner...