An **Arithmetic progression** or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms
is constant.
The arithmetic progression can be finite or infinite.

The *n*th term (a_{n}) of the sequence is given by:

where,

a_{1}ā initial term of an arithmetic progression;

dā common difference of successive members;

nā 1, 2, 3 ...

The sum of the first *n* members is called **arithmetic series**:

$$S_{n}=\frac{n}{2}\times(a_{1}+a_{n})=\frac{n}{2}\times\left [2a_{1}+(n-1)d \right ]$$

The standard deviation of any arithmetic progression can be calculated as:

$$\sigma=\left |d \right |\times\sqrt{\frac{(n+1)(n+1)}{12}}$$

### See also: