# Arithmetic Sequence **An *Arithmetic Sequence***, or progression, **is a kind of a number sequence where the difference of two adjacent terms is constant.** That difference is called the *common difference* $d$. The sequence starts with an *initial term* $a_1$. The recursive definition of an arithmetic sequence is thus $a_n = a_{n-1} + d$, and the explicit formula is: $a_n = a_1 + (n-1)d$. Sequences with a common ratio, instead of a common difference, are called the [[Geometric Sequence]]-s. ![[Arithmetic Series#^3b0qf5]]