# Definition of *arithmetic progression* in English:

## arithmetic progression

Syllabification: ar·ith·met·ic pro·gres·sionPronunciation: /ˌariTHˈmetik prəˈgreSHən
/

(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.

## More definitions of **arithmetic progression**

Definition of **arithmetic progression**in:

- The British & World English dictionary