The formula a_n = a_1 * r^(n-1) represents the n -th term of a geometric sequence. In this equation, a_n is the term we want to find, a_1 is the first term, r is the common ratio, and n is the term number. The common ratio r is the factor by which we multiply each term to get the next term in the sequence. For example, if the first term a_1 is 2 and the common ratio r is 3, the sequence would be 2, 6, 18, 54, and so on. Here, each term is obtained by multiplying the previous term by 3. This formula is useful in various fields, including finance and science, to model exponential growth or decay.