# arithmetic progression

Line breaks: arith|met¦ic pro|gres¦sion
(also arithmetic series)

## Definition of arithmetic progression in English:

### noun

1A sequence of numbers in which each differs from the preceding one by a constant quantity (e.g. 1, 2, 3, 4, etc.; 9, 7, 5, 3, etc.).
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.
1.1 [mass noun] The relation 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:

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= trending

## More on arithmetic progression

### More words in this category

arithmetic mean asymptote division equivalent factor
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Pronunciation: rɪˈzɪlɪənt