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 {\displaystyle a_{1}} and the common difference of successive members is d , then the n th term of the sequence ( {\displaystyle a_{n}} ) is given by: {\displaystyle \ a_{n}=a_{1}+(n-1)d} , and in general {\displaystyle \ a_{n}=a_{m}+(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 ...
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