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 $d$, which is known as the difference of this progression. Thus, each arithmetic progression has the form
in which the general term is
A characteristic property of an arithmetic progression is
If $d>0$, the progression is increasing; if $d<0$, it is decreasing. The simplest example of an arithmetic progression is the series of natural numbers $1,2,\ldots$. The number of terms of an arithmetic progression can be bounded or unbounded. If an arithmetic progression consists of $n$ terms, its sum can be calculated by the formula:
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=29401