Which type of sequence involves multiplying each term by a constant ratio?

The type of sequence that involves multiplying each term by a constant ratio is the geometric progression. In this sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. This creates a pattern in which the terms can grow or decrease exponentially depending on whether the common ratio is greater than or less than one.

For example, if the first term is 2 and the common ratio is 3, the subsequent terms would be 2, 6, 18, 54, and so on. Each term is obtained by multiplying the previous term by 3. This characteristic of having a constant multiplicative relationship distinguishes geometric progressions from other types of sequences, such as arithmetic progressions, where the change between terms is based on addition or subtraction, and quadratic sequences, which are defined by a second-degree polynomial. Harmonic progressions involve reciprocals of an arithmetic progression, further distinguishing them from geometric patterns.