An arithmetic sequence (sometimes called a “progression”) is a particular type of sequence that has an initial value, as with all sequences. A proper arithmetic sequence has a common difference, that when added to the initial number and each consecutive number, provides the arithmetic sequence. Keep in mind that this common difference can be a positive or a negative value so the arithmetic sequence might be increasing or decreasing regularly. In addition, an arithmetic sequence may begin with a negative number as long as the sequence progresses by the constant value from that starting point.

An arithmetic sequence example would look like this:

1, 5, 9, 13, 17, 21, 25, 29, … with a common difference of 4.

Look for the common difference by subtracting the preceding value from the current value and ensuring this holds for the following numbers.