Explain how to find the general term of a geometric sequence.

To find the general term of a geometric sequence, use the formula an = a1 * r^(n-1).

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio, called the common ratio (r). The first term is denoted as a1, the second term as a2, and so on. The general term of a geometric sequence is denoted as an.

To find the general 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 any term in the sequence.

For example, consider the geometric sequence 2, 4, 8, 16, 32, ... where a1 = 2 and r = 2. To find the 6th term (a6), we can use the formula:

a6 = a1 * r^(6-1)
a6 = 2 * 2^(6-1)
a6 = 2 * 2^5
a6 = 2 * 32
a6 = 64

Therefore, the 6th term of the sequence is 64.

It is important to note that the formula for the general term of a geometric sequence only works if the ratio between consecutive terms is constant. If the ratio is not constant, then the sequence is not geometric and the formula cannot be used.