# Arithmetic Progression

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 nth term (an) of the sequence is given by:

$$a_{n}=a_{1}+(n-1)d$$

where,

a1— initial term of an arithmetic progression;
d— common difference of successive members;
n— 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:

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