# Arithmetic progression

Keywords: 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:

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

The sum of the first n terms:

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