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.