Determine the nth term of a geometric sequence.

To determine the nth term of a geometric sequence, use the formula an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant factor called the common ratio. For example, the sequence 2, 4, 8, 16, 32 is a geometric sequence with a common ratio of 2.

To find the nth term of a geometric sequence, you need to know the first term (a1) and the common ratio (r). Once you have these values, you can use the formula an = a1 * r^(n-1) to find the nth term.

For example, let's say you have a geometric sequence with a first term of 3 and a common ratio of 2. To find the 5th term of the sequence, you would use the formula:

a5 = a1 * r^(n-1)
a5 = 3 * 2^(5-1)
a5 = 3 * 2^4
a5 = 3 * 16
a5 = 48

Therefore, the 5th term of the sequence is 48.

It's important to note that the formula for the nth term of a geometric sequence only works if the sequence is truly geometric. In other words, each term must be found by multiplying the previous term by the same constant factor. If the sequence is not geometric, this formula will not work.