Arithmetic Progression

Definition: Arithmetic Progression

Arithmetic Progression

Noun

1. (math) a progression in which a constant is added to each term in order to obtain the next term; "1-4-7-10-13- is the start of an arithmetic progression".

Specialty Definition: Arithmetic Progression

Domain	Definition
Mathematics	A sequence of numbers in which each term is greater than its predecessor by a constant d, called the common difference. Source: European Union. (references)
Source: compiled by the editor from various references; see credits.

Specialty Definition: Arithmetic progression

In mathematics, an arithmetic progression is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, ... is an arithmetic progression with common difference 2.

If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the n-th term of the sequence is given by

a + nd, n = 0, 1, 2, ... if the initial term is taken as the 0th
a + (n-1)d, n = 1, 2, ... if the initial term is taken as the 1st

The first option gives an easier formula, but uses a somewhat confusing terminology.

The sum of the numbers in an arithmetic progression is called an arithmetic series. A convenient formula for arithmetic series is available.

See also geometric progression.

Frequency of Internet Keywords: Arithmetic Progression

Modern Translation: Arithmetic Progression

Language		Translations for "arithmetic progression"; alternative meanings/domain in parentheses.
Arabic		‏المتوالية العددية. (various references)

Dutch		rekenkundige rij (arithmetic sequence). (various references)

French		suite arithmétique (arithmetic sequence), progression arithmétique (arithmetical progression). (various references)

German		arithmetische Reihe (arithmetic series, arithmetical progression). (various references)

Italian		progressione aritmetica (arithmetic sequence). (various references)

Japanese Kanji		等差数列 . (various references)

Japanese Katakana		とうさすうれつ. (various references)

Pig Latin		arithmeticay ogressionpray

Spanish		progresión aritmética (arithmetic sequence). (various references)
Source: compiled by the editor from various translation references.

Anagrams: Arithmetic Progression

Scrabble® Enable2K-Verified Anagrams
	Words within the letters "a-c-e-e-g-h-i-i-i-m-n-o-o-p-r-r-r-s-s-t-t"
	-5 letters: preregistrations, reorchestrations.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.