Which sequence is characterized by multiplying or dividing by the same number?

In mathematics, a geometric sequence is defined as a sequence of numbers where each term after the first is found by multiplying or dividing the previous term by a fixed, non-zero number called the common ratio. This characteristic is what distinguishes a geometric sequence from other types of sequences.

For example, in the geometric sequence 2, 6, 18, 54, each term is obtained by multiplying the previous term by 3. Conversely, if you took a sequence like 64, 16, 4, which decreases, each term can be derived by dividing the previous term by 4. The key feature here is the consistent application of multiplication or division across the entire sequence, leading to exponential growth or decay.

In contrast, an arithmetic sequence increases or decreases by adding or subtracting a constant value (the common difference) instead of multiplying or dividing. The other options refer to different mathematical concepts: the order of operations sets rules for how to evaluate expressions, while a variable expression involves a combination of numbers, variables, and operations, but does not pertain to a sequence. Thus, the defining property of the geometric sequence makes it the correct answer to the question.