arithmetic progression

American  

noun

1. a sequence in which each term is obtained by the addition of a constant number to the preceding term, as 1, 4, 7, 10, 13, and 6, 1, −4, −9, −14.

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arithmetic progression British  

noun

1. a sequence of numbers or quantities, each term of which differs from the succeeding term by a constant amount, such as 3,6,9,12 Compare geometric progression

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arithmetic progression Scientific  

/ ăr′ĭth-mĕt′ĭk /

1. A sequence of numbers such as 1, 3, 5, 7, 9 …, in which each term after the first is formed by adding a constant (in this case, 2) to the preceding number.

2. Compare geometric progression

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Etymology

Origin of arithmetic progression

First recorded in 1585–95

Example Sentences

The congruum in our first example is 24, and the three squares in arithmetic progression are 12, 52, and 72.

From Scientific American

An arithmetic progression is a sequence in which the difference between numbers remains constant.

From Washington Post

This technique reduces the time required to solve a problem in a binary fashion by halves, rather than in arithmetic progression one small step at a time.

From Project Gutenberg

An arithmetic progression is a sequence of numbers with the same differences between successive numbers: 1, 3, 5, 7 is an arithmetic progression with difference 2, for example.

From Scientific American

Early mathematicians recognized that when three squares occurred in arithmetic progression this way, the square root of the middle number — in this case, 5 — is the hypotenuse of the right triangle.

From Scientific American