What defines a geometric sequence?

• A. A sequence where each term is added by a fixed number
• B. A sequence of numbers where each term is found by multiplying the previous term by a fixed, non-zero number
• C. A sequence where every term is a prime number
• D. A linear relation represented by arithmetic progression

Answer: (B)

A geometric sequence is defined by the property that each term is derived from the previous term by multiplying it by a constant, non-zero factor, known as the common ratio. This characteristic means that if you have the first term, you can find any subsequent term by repeatedly applying this multiplication. For example, if the first term is 2 and the common ratio is 3, the sequence would be 2, 6, 18, 54, and so on, since each term is obtained by multiplying the previous term by 3.

In contrast to a geometric sequence, other types of sequences or definitions provided do not capture this multiplication aspect. A sequence where each term is added by a fixed number describes an arithmetic sequence, which relies on addition rather than multiplication. A sequence consisting exclusively of prime numbers does not focus on the relationship between terms in the same way that a geometric sequence does. Similarly, a linear relation represented by arithmetic progression pertains specifically to sequences defined through addition and does not involve multiplication, which is essential in defining a geometric sequence.