Which statement describes a geometric sequence?

• A. A sequence in which each term is found by multiplying the previous term by the same number
• B. A sequence that adds a constant to get the next term
• C. A sequence with alternating signs
• D. A sequence with decreasing values only

Answer: (A)

Geometric sequences are built by multiplying the previous term by the same number each step. That constant multiplier, called the common ratio, determines how the sequence grows or shrinks from term to term. For example, starting with 2 and multiplying by 3 gives 2, 6, 18, 54, and so on, illustrating the consistent multiplicative pattern.

This differs from an arithmetic sequence, where you add the same amount each time. A sequence described with alternating signs indicates a pattern of signs rather than the rule for creating each term. A sequence that only decreases would be a special case if the ratio is between 0 and 1, but geometric sequences can also increase when the ratio is greater than 1, so that description isn’t defining the pattern.