Which sequence of numbers takes the general form: an = a + (n-1)d?

The sequence described by the formula an = a + (n-1)d is known as an arithmetic progression. In this formula, "a" represents the first term of the sequence, "d" represents the common difference between consecutive terms, and "n" indicates the term number in the sequence.

An arithmetic progression is characterized by a constant difference between each term. That means, if you start with the first term "a" and repeatedly add the common difference "d," you can generate the entire sequence. For example, if "a" is 2 and "d" is 3, the sequence becomes 2, 5, 8, 11, and so on, where each term increases by 3 from the previous term.

In contrast, other types of sequences, such as geometric progressions, involve multiplying a common ratio rather than adding a common difference. Harmonic progressions involve taking the reciprocal of terms in an arithmetic sequence and a quadratic progression does not follow a linear pattern governed by a constant addition but rather a second-degree polynomial relationship. Thus, the structure defined by an = a + (n-1)d unmistakably identifies this as an arithmetic progression.