Determine the nth term of an arithmetic sequence.

To determine the nth term of an arithmetic sequence, use the formula: an = a1 + (n-1)d.

An arithmetic sequence is a sequence of numbers where each term is obtained by adding a fixed number (called the common difference) to the previous term. For example, 2, 5, 8, 11, 14 is an arithmetic sequence with a common difference of 3.

To find the nth term of an arithmetic sequence, you need to know the first term (a1) and the common difference (d). Once you have these values, you can use the formula: an = a1 + (n-1)d.

For example, let's say you want to find the 10th term of the arithmetic sequence 3, 7, 11, 15, 19, ... To use the formula, you need to know the first term (a1) and the common difference (d). In this case, a1 = 3 and d = 4 (since each term is obtained by adding 4 to the previous term).

Now you can plug these values into the formula: a10 = a1 + (10-1)d = 3 + 9(4) = 39. Therefore, the 10th term of the sequence is 39.

It's important to note that the formula only works for arithmetic sequences, and not for other types of sequences (such as geometric sequences). If you're not sure what type of sequence you're dealing with, you may need to use other methods to find the nth term.