What is the formula for the nth term in an arithmetic sequence?

The formula for the nth term in an arithmetic sequence accurately captures how the terms are generated based on the first term and the common difference. The correct formula is expressed as a_n = a_1 + (n-1)d, where:

• a_n represents the nth term of the sequence.

• a_1 is the first term.

• d is the common difference between consecutive terms.

• (n-1) indicates how many increments of the common difference are added to the first term to get to the nth term.

This formula works because, in an arithmetic sequence, each term is the previous term plus a constant difference (d). To find the nth term, you take the first term and add the common difference multiplied by the number of steps to reach that term, which is n - 1 since you start counting from the first term.

The other options fail to adhere to that structure or misrepresent the relationship between the terms of an arithmetic sequence. For example, simply adding 4d does not generalize correctly for any nth term unless it is explicitly stated that the common difference is 4, which is not the case for all arithmetic sequences. Similarly, simply adding n*d or multiplying a_1 by d does not account for the