What is "arithmetic progression"

n. (context analysis English) A sequence in which each term except the first is obtained from the previous by adding a constant value, known as the common difference of the arithmetic progression.

n. (mathematics) 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"

In mathematics, an '''arithmetic progression ''' (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.

If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the nth term of the sequence (a) is given by:

a = a + (n − 1)d, 

and in general

a = a + (n − m)d.

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.

The behavior of the arithmetic progression depends on the common difference d. If the common difference is:

• Positive, then the members (terms) will grow towards positive infinity.
• Negative, then the members (terms) will grow towards negative infinity.