What is the eighth term of the geometric pattern whose first term is 5 and whose fourth term is 1/25?a.65b.5^-6c.5d.5^-1

The eighth term of a geometric sequence can be found using the formula a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

First, we need to find the common ratio (r). We know that the first term (a_1) is 5 and the fourth term (a_4) is 1/25. We can use the formula to find r:

1/25 = 5 * r^(4-1) 1/25 = 5 * r^3 r^3 = 1/125 r = (1/125)^(1/3) r = 1/5

Now that we have the common ratio, we can find the eighth term (a_8) using the formula:

a_8 = a_1 * r^(8-1) a_8 = 5 * (1/5)^7 a_8 = 5 * 1/78125 a_8 = 1/15625

So, the eighth term of the geometric sequence is 1/15625, which is not listed in the options. There might be a mistake in the question or the options.