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Arithmetic sequences and sums

A sequence of numbers such that the difference between the consecutive terms is a constant is called arithmetic progression or arithmetic sequence.

For example, the sequence 2, 5, 8, 11, 14, 17, 20, . . . is an arithmetic progression with a common difference of 3.

Rule of arithmetic sequence

General rule of arithmetic sequence can be written by this formula, where $a_1$ - the first term, $d$ - the difference between the terms, $n$ - the number of term.

$$a_n=a_1+(n-1)d$$

Sum of arithmetic sequence

To sum up the terms of an arithmetic sequence is simple only when we have not many terms. But for sequences that have large number of terms we can use this formula below.

$$S_n=\frac{2a_1+(n-1)d}{2}n$$

2020-12-02