What is the definition of a geometric sequence?

The definition of a geometric sequence accurately describes it as a sequence where each term is multiplied by a constant factor to obtain the next term. This constant factor is known as the common ratio. For example, in a geometric sequence like 2, 6, 18, 54, the common ratio is 3, since each term is three times the previous term. This multiplication by a constant differentiates geometric sequences from arithmetic sequences, where a fixed number is added to generate the next term. Understanding this distinction is crucial for recognizing the characteristics of geometric sequences and applying this knowledge in various mathematical contexts.