Formulas and properties of arithmetic sequence

Arithmetic sequence (arithmetic progression) — a sequence of numbers a₁, a₂, a₃, ..., in which each member, starting with the second, equal to the sum of the previous member and a constant number d, called the common difference.

n -th term of the sequence is given by

a_n = a₁ + (n - 1)d

a_n = a_{n - 1} + d

Common difference

d = a_n - a_{n - 1}

The sum of a finite arithmetic progression is called an arithmetic series.

Formulas of arithmetic series

Sn =	(a1 + an) · n
	2

Sn =	2a1 + (n - 1) d	· n
	2

Properties of arithmetic sequence

an =	an + 1 + an - 1
	2