Geometric progression

Alongside the arithmetic progression, in which a constant is added, sits the geometric progression, in which at each step one multiplies by a constant.

Definition — Geometric progression (GP)

A geometric progression is a sequence $(a_n)$ in which each term is obtained from the previous one by multiplying by a constant $q\ne 0$, called the common ratio: $a_{n+1} = q\,a_n,\qquad q\in\mathbb{R}\setminus\{0\}.$ The closed form of the $n$-th term is $a_n = a_1\,q^{n-1}.$

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Topics: Sequences
Concepts: Geometric progression · Common ratio · General term