How do you find a formula for the nth term of the geometric sequence: 500, 100, 20, 4, …?

To find a formula for the nth term of a geometric sequence, you need to determine the common ratio (r) between consecutive terms. In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio.

In your sequence, the first term is 500, and the second term is 100. To find the common ratio, you can divide the second term by the first term:

r = 100 / 500 = 1/5

Now that you know the common ratio (r = 1/5), you can use it to find the nth term formula for the sequence. The nth term formula for a geometric sequence is:

a_n = a_1 * r^(n-1)

In this formula:

a_n represents the nth term you want to find.
a_1 is the first term of the sequence (500 in this case).
r is the common ratio (1/5 in this case).
n is the term number you want to find.
So, for your sequence, the nth term formula would be:

a_n = 500 * (1/5)^(n-1)

You can use this formula to find any term in the sequence by plugging in the value of n. For example, if you want to find the 5th term, you would plug in n = 5:

a_5 = 500 * (1/5)^(5-1)
a_5 = 500 * (1/5)^4
a_5 = 500 * (1/625)
a_5 = 500/625
a_5 = 4/5

So, the 5th term of the sequence is 4/5.