Which sequence describes the term values in a defined arithmetic series?

The correct choice accurately reflects the formula for the (n)-th term of an arithmetic series. In an arithmetic series, each term is derived from the previous one by adding a constant difference, denoted as (d). The formula (a_n = a_1 + (n-1)d) expresses this relationship clearly:

• (a_n) represents the (n)-th term of the sequence.

• (a_1) is the first term in the sequence.

• (d) is the common difference between consecutive terms.

• (n) indicates the position of the term within the sequence.

By employing this formula, any term in the arithmetic series can be calculated, as it straightforwardly combines the starting point, (a_1), with the total amount added, which is the product of ((n-1)) and (d). This effectively captures the linear nature of an arithmetic series.

The other options describe different types of sequences. For instance, the polynomial expression in one option is characteristic of quadratic sequences, while the one involving exponential growth is indicative of a geometric sequence. The factorial sequence represents exponential growth but does not align with the linear progression of an arithmetic sequence. Each