In mathematics, the notation a_n represents a sequence of numbers where n indicates the position of each number in the sequence. For example, a_1 is the first number, a_2 is the second, and so on. Each term can depend on the previous terms, creating a pattern or rule that defines the entire sequence. The term a_{n-1} refers to the number that comes just before a_n in the sequence. This relationship is crucial for understanding how sequences work, as it shows how each term can be derived from its predecessor. For instance, if a_n is defined as a_n = a_{n-1 + 2}, each term increases by 2 from the previous one.