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

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

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

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

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

If the common ratio (r) is less than 1, the sequence will approach zero as n approaches infinity. If the common ratio is greater than 1, the sequence will increase without bound as n approaches infinity. If the common ratio is equal to 1, the sequence is simply a constant sequence.