# Geometric Sequence A *geometric sequence*, or progression, **is a number sequence where the ratio of two adjacent terms is constant**. That ratio is called the *common ratio* $r$. ^ep8vl9 The recursive definition of an element in a geometric sequence is thus $a_n = a_{n-1} r$, and the explicit formula for the $n$-th element is: $a_n = r^n$. Sequences with a common difference, instead of a common ratio, are called the [[Arithmetic Sequence]]-s. ![[Geometric Series#^4zycdx]] ![[Geometric Infinite Series#^45eu81]]