Formulas and properties of arithmetic sequence
Definition Arithmetic sequence ( arithmetic progression) — a sequence of numbers a_{1}, a_{2}, a_{3}, ..., 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} = a_{1} + (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
S_{n} = |
(a_{1} + a_{n}) · n | 2 |
S_{n} = |
2a_{1} + (n - 1) d |
· n |
2 |
Properties of arithmetic sequence
a_{n} = |
a_{n + 1} + a_{n - 1} |
2 |
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