Final answer:
A geometric sequence is created by multiplying each term by a non-zero constant, known as the common ratio, not by adding or subtracting. The sequence grows exponentially based on this constant multiplication.
Step-by-step explanation:
A geometric sequence is a sequence in which each term after the first is obtained by multiplying the preceding term by a non-zero constant. This constant is known as the common ratio. For example, if we have a geometric sequence where the first term is 2 and the common ratio is 3, the sequence would be 2, 6, 18, 54, and so forth. Each term is obtained by multiplying the previous term by 3. This is different from an arithmetic sequence where each term is obtained by adding (or subtracting) a constant difference.
The commutative property of addition (A+B=B+A) which holds true for the addition of ordinary numbers, as in the example 2 + 3 = 3 + 2, does not apply to sequences since geometric sequences rely on multiplication for each successive term. When dealing with geometric sequences, the pattern follows a multiplication chain of the same number, which is equivalent to raising the base to a power—the power equaling the number of times the base appears in the chain.