The formula a_n = a_1 + (n-1)d is used to find the n -th term of an arithmetic sequence. In this formula, a_n represents the n -th term, a_1 is the first term, d is the common difference between consecutive terms, and n is the term number. For example, if the first term a_1 is 3 and the common difference d is 2, the sequence would be 3, 5, 7, 9, and so on. To find the 5th term, you would substitute n = 5 into the formula, resulting in a_5 = 3 + (5-1) \cdot 2 = 11 .