What distinguishes a geometric series?

A geometric series is characterized by the property that each term is generated by multiplying the previous term by a fixed, non-zero constant called the common ratio. This common ratio does not change throughout the series, allowing the sequence to grow or shrink exponentially. For instance, if the first term is (a) and the common ratio is (r), the terms of the series can be expressed as (a, ar, ar^2, ar^3, \ldots).

The other options describe different types of sequences or series. For example, the first option refers to a series where each term is a sum of the previous terms, which characterizes recursive sequences such as the Fibonacci sequence. The second option suggests uniqueness in values but doesn’t capture the essence of how terms are generated in a geometric series. The fourth option involves a fixed reduction, which fits an arithmetic series instead, where each term is formed by adding or subtracting a constant value from the previous term.

Understanding the definition of a geometric series helps clarify how the terms relate to one another through multiplication by a constant, emphasizing the exponential growth or decay based on the common ratio.