# Arithmetic progression

Arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For example: 1, 3, 5,.....,11,13,15,...

$${a}_{1},{a}_{2},{a}_{3},...,{a}_{n-1},{a}_{n},{a}_{n+1},...$$

**n-th term of the sequence:**

$${a}_{n}={a}_{1}+(n-1)d$$

$${a}_{n}=\frac{{a}_{n-1}+{a}_{n+1}}{2},\text{}\text{}n1$$

**The sum of the first n terms:**

$${S}_{n}=\frac{\left({a}_{1}+{a}_{n}\right)\xb7n}{2}$$

$${S}_{n}=\frac{[2{a}_{1}+(n-1\left)d\right]\xb7n}{2}$$

Keywords: Arithmetic progression