arithmetic sequence

An arithmetic sequence is a sequence where a subsequent element is the previous element summed with a constant value called the common difference.

Formally,

a_{n + 1} = a_{n} + d

a_{n} = a_{k} + d (n - k)

The partial sum of an arithmetic sequence is

\sum_{k = 0}^{n} a + d k = \frac{n}{2} (2 a + d n)

where $(2 a + d n)$ is the first term plus the $n^{t h}$ term.