Common ratio - (College Algebra) - Vocab, Definition, Explanations | Fiveable

Definition

The common ratio is the constant factor between consecutive terms of a geometric sequence. It is found by dividing any term by its preceding term.

The common ratio can be positive, negative, or a fraction.
In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio.
If the common ratio is greater than 1, the terms of the sequence will increase; if it's between 0 and 1, they will decrease.
The formula for the $n$-th term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term and $r$ is the common ratio.
For an infinite geometric series to converge, the absolute value of the common ratio must be less than 1.

A sequence in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

A series whose partial sums approach a finite limit as more terms are added.

The sum of terms in a geometric sequence.