Definition of arithmetic sequence


An arithmetic sequence , also called arithmetic progression, is a number pattern in which the difference between consecutive terms or numbers is constant or the same.


Example #1

2, 5, 8, 11, 14, ... is an arithmetic sequence because the difference between any two consecutive numbers is 3.

5 - 2 = 3

8 - 5 = 3

11 - 8 = 3

14 - 11 = 3

and so forth ...

In the example above, the sequence increased by the same amount each term. In the example below, we show that the sequence can also decrease by the same amount each term.


Example #2

40, 35, 30, 25, 20, 15 , ... is an arithmetic sequence because the difference between any two consecutive numbers is -5.

35 - 40 = -5

30 - 35 = -5

25 - 30 = -5

and so forth ...

The number 3 or the number -5  in the examples above is called a common difference. The common difference is positive if the terms of the sequence are increasing or negative if the terms of the sequence are decreasing.

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