What defines a geometric sequence?

A geometric sequence is defined by the property that each term is obtained by multiplying the previous term by a fixed, non-zero number known as the common ratio. This constant ratio can result in terms that progressively increase or decrease in size, depending on the value of the common ratio. For instance, in the sequence 2, 6, 18, 54, each term is multiplied by 3 to arrive at the next term.

This characteristic of constant multiplication contrasts with an arithmetic sequence, where each term has a constant difference added to it. While sequences can have identical terms or patterns of linear increase, these do not capture the essence of a geometric sequence, which fundamentally relies on the multiplication aspect. Thus, the correct answer highlights the unique feature of the relationship between the terms in a geometric sequence.