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Formulas and properties of arithmetic sequence

Definition
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

an = a1 + (n - 1)d

an = an - 1 + d

Common difference

d = an - an - 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

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