Common ratio

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.

5 Must Know Facts For Your Next Test

1. The common ratio can be positive, negative, or a fraction.
2. In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio.
3. 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.
4. 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.
5. For an infinite geometric series to converge, the absolute value of the common ratio must be less than 1.

Review Questions

• What is the formula to find the $n$-th term in a geometric sequence?
• How do you determine if a series converges based on its common ratio?
• If you know two consecutive terms in a geometric sequence, how do you find the common ratio?

Related terms

Geometric Sequence: 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.

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

Geometric Series: The sum of terms in a geometric sequence.