What is a sequence in mathematics?

A sequence in mathematics refers to a list of numbers that are arranged in a particular order based on a defined pattern or rule. This sequence can consist of numbers that increase or decrease consistently, such as an arithmetic sequence where each term is derived from adding or subtracting the same value, or a geometric sequence where each term is obtained by multiplying or dividing by a constant.

The key aspect of a sequence is its orderly arrangement and the relationship between the numbers involved, which distinguishes it from simple collections or sets of numbers that do not exhibit a specific ordering. In contrast, a single number does not encapsulate the concept of a sequence since it lacks any additional numbers to form a pattern. Similarly, an equation without a solution does not relate to sequences, as it pertains to algebraic expressions rather than ordered lists. Lastly, while ratios involve comparisons between pairs of numbers, they do not inherently imply a sequence unless defined by a specific pattern. Thus, the correct understanding of a sequence effectively aligns with the definition provided in the context of the selected choice.