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Let's examine the sequence \(100, 20, 4, \frac{4}{5}\).

To find the general formula or pattern, note how the terms change:

1. From \(100 \to 20\), we divide by \(5\).
2. From \(20 \to 4\), we divide by \(5\).
3. From \(4 \to \frac{4}{5}\), we again divide by \(5\).

Thus, the sequence is a geometric progression with the first term \(a = 100\) and a common ratio \(r = \frac{1}{5}\).

The formula for the \(n\)-th term of a geometric sequence is:
\[
a_n = a \cdot r^{n-1}
\]
Substituting \(a = 100\) and \(r = \frac{1}{5}\), we get:
\[
a_n = 100 \cdot \left(\frac{1}{5}\right)^{n-1}
\]
For the 8th term (\(n = 8\)):
\[
a_8 = 100 \cdot \left(\frac{1}{5}\right)^7 = 100 \cdot \frac{1}{78125} = \frac{100}{78125}
\]
Simplifying:
\[
a_8 = \frac{4}{3125}
\]
This matches one of the options.

The correct answer is:
\[
\boxed{\frac{4}{3125}}
\]

Would you like further details on this solution or another topic?

Here are 5 related questions to explore:
1. What is a geometric progression?
2. How do you determine the common ratio in a sequence?
3. What is the formula for the sum of a finite geometric series?
4. How can you convert a decimal into a fraction?
5. How do you find the general term of an arithmetic sequence?

**Tip**: Always check if a sequence has a constant ratio or difference to identify if it's geometric or arithmetic.

Find the 8th term of the sequence 100, 20, 4, 4/5.

Learn how to find the 8th term of a geometric sequence with the first term of 100 and a common ratio of 1/5. This step-by-step guide explains the geometric sequence formula and how to apply it for middle and high school students.

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