# Definition:Geometric Sequence/Finite

## Definition

A finite geometric sequence is a geometric sequence with a finite number of terms .

### Extremes of Finite Geometric Sequence

Let $G_n = \sequence {a_0, a_1, \ldots, a_n}$ be a finite geometric sequence.

The extremes of $G_n$ are the terms $a_0$ and $a_n$ of $G_n$.

### Initial Term

Let $G = \left\langle{a_0, a_1, \ldots}\right\rangle$ be a geometric sequence.

The initial term of $G_n$ is the term $a_0$.

The same definition applies to a finite geometric sequence $G_n = \sequence {a_0, a_1, \ldots, a_n}$.

### Final Term

Let $G_n = \sequence {a_0, a_1, \ldots, a_n}$ be a finite geometric sequence.

The final term of $G_n$ is the term $a_n$.