Arithmetic progression
arithmetic series of the first order
A sequence of numbers in which each term is obtained from the term immediately preceding it by adding to the latter some fixed number , which is known as the difference of this progression. Thus, each arithmetic progression has the form
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in which the general term is
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A characteristic property of an arithmetic progression is
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If , the progression is increasing; if
, it is decreasing. The simplest example of an arithmetic progression is the series of natural numbers
. The number of terms of an arithmetic progression can be bounded or unbounded. If an arithmetic progression consists of
terms, its sum can be calculated by the formula:
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Comments
For results on prime numbers in arithmetic progressions see Distribution of prime numbers.
Arithmetic progression. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Arithmetic_progression&oldid=12826