What do the terms of a geometric sequence have in common?

In a geometric sequence, each term is generated by multiplying the previous term by a constant factor, often referred to as the common ratio. This characteristic distinguishes geometric sequences from other types of sequences, such as arithmetic sequences, where a constant is added to each term.

For example, if the first term of a geometric sequence is 3 and the common ratio is 2, the sequence would be 3, 6, 12, 24, and so on, where each term results from multiplying the previous term by 2. This consistent multiplication leads to the exponential growth of the sequence.

Understanding this property is crucial for handling problems related to geometric sequences, including finding the nth term or the sum of the terms. Multiplying by a constant factor provides a clear pattern that students can recognize and use effectively in various mathematical contexts.