Sequence of numbers in which the difference

*r*between two consecutive terms is constant.Synonym for arithmetic progression.

The constant difference between two consecutive terms is called the difference of the arithmetic sequence.

### Example

Consider the number sequence S = {1, 3, 5, 7, 9, 11, …}

Notice that there is a constant difference of 2 between two consecutive terms. This means that it is an arithmetic sequence defined by: S = {*x* ∈ \(\mathbb {N}\) | *x* = 2*r* + 1}.