Which of the following best defines a geometric sequence?

Which of the following best defines a geometric sequence?

• A. A sequence based on addition.
• B. A sequence based on multiplication.
• C. A sequence of prime numbers.
• D. A sequence of whole numbers.

Answer: (B)

A geometric sequence is best defined as a sequence in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. This means that the relationship between consecutive terms is multiplicative rather than additive, which distinguishes it from other types of sequences, such as arithmetic sequences, where the terms are based on addition of a constant. In a geometric sequence, if the first term is \( a \) and the common ratio is \( r \), the sequence can be represented as \( a, ar, ar^2, ar^3, \ldots \). This consistent multiplicative pattern is the defining characteristic of a geometric sequence, making answer choice B the correct definition. The other options do not capture this defining feature: a sequence based on addition refers to arithmetic sequences, while a sequence of prime numbers and a sequence of whole numbers are not specifically tied to the concept of multiplicative relationships.

A geometric sequence is best defined as a sequence in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. This means that the relationship between consecutive terms is multiplicative rather than additive, which distinguishes it from other types of sequences, such as arithmetic sequences, where the terms are based on addition of a constant.

In a geometric sequence, if the first term is ( a ) and the common ratio is ( r ), the sequence can be represented as ( a, ar, ar^2, ar^3, \ldots ). This consistent multiplicative pattern is the defining characteristic of a geometric sequence, making answer choice B the correct definition.

The other options do not capture this defining feature: a sequence based on addition refers to arithmetic sequences, while a sequence of prime numbers and a sequence of whole numbers are not specifically tied to the concept of multiplicative relationships.