Which formula represents the nth term of an arithmetic sequence?

The formula for the nth term of an arithmetic sequence is based on the first term and the common difference. In an arithmetic sequence, each term is generated by adding the common difference to the previous term.

The nth term can be expressed as the first term, denoted as 'a', plus the product of the common difference 'd' and the number of terms subtracted by one (since the sequence starts counting from the first term). This leads to the formula:

nth term = a + (n - 1)d.

This concise relationship captures how each subsequent term in the sequence relates to the initial term and the regular spacing of the terms given by the common difference.

The other choices represent different mathematical concepts:

• One choice computes the sum of the first n terms of an arithmetic sequence, which is not relevant to finding the nth term itself.
• Another choice reflects a formula for the sum of a geometric series, which is entirely different from the context of an arithmetic sequence.
• The last choice incorrectly utilizes division in a way that does not fit the format for calculating terms in an arithmetic sequence.

Thus, the provided formula successfully encapsulates the relationship needed to find any specific term in an arithmetic sequence.