Let's analyze the sequence provided: \( \frac{1}{2}, \frac{1}{2}, \frac{3}{8}, \frac{1}{4}, \frac{5}{32} \).

To find the 6th, 7th, and 8th terms, we need to identify a pattern or formula governing the sequence.

### Observing the pattern:

1. The first two terms are identical: \( \frac{1}{2} \).
2. From the second to the third term:
   \[
   \frac{1}{2} \rightarrow \frac{3}{8}
   \]
   We can express \( \frac{1}{2} \) as \( \frac{4}{8} \), so the transition is \( \frac{4}{8} \rightarrow \frac{3}{8} \), which is a decrease by \( \frac{1}{8} \).
3. From the third to the fourth term:
   \[
   \frac{3}{8} \rightarrow \frac{1}{4}
   \]
   We can express \( \frac{1}{4} \) as \( \frac{2}{8} \), so the transition is \( \frac{3}{8} \rightarrow \frac{2}{8} \), which is another decrease by \( \frac{1}{8} \).
4. From the fourth to the fifth term:
   \[
   \frac{1}{4} \rightarrow \frac{5}{32}
   \]
   Expressing \( \frac{1}{4} \) as \( \frac{8}{32} \), the transition is \( \frac{8}{32} \rightarrow \frac{5}{32} \), which is a decrease by \( \frac{3}{32} \).

Given these observations, it appears that each subsequent term is obtained by subtracting a progressively smaller fraction.

### To calculate the 6th term:

Following the pattern of decreasing fractions, subtracting \( \frac{1}{32} \) from the last known fraction:
\[
\frac{5}{32} - \frac{1}{32} = \frac{4}{32} = \frac{1}{8}
\]
Thus, the 6th term is \( \frac{1}{8} \).

### To calculate the 7th term:

Continuing the pattern, we subtract another fraction (possibly smaller):
\[
\frac{1}{8} - \frac{1}{16} = \frac{2}{16} - \frac{1}{16} = \frac{1}{16}
\]
So, the 7th term is \( \frac{1}{16} \).

### To calculate the 8th term:

The subtraction pattern continues:
\[
\frac{1}{16} - \frac{1}{32} = \frac{2}{32} - \frac{1}{32} = \frac{1}{32}
\]
Thus, the 8th term is \( \frac{1}{32} \).

### Summary:
- 6th term: \( \frac{1}{8} \)
- 7th term: \( \frac{1}{16} \)
- 8th term: \( \frac{1}{32} \)

Would you like any further details or have any questions about this sequence?

#### Related Questions:
1. What would be the 9th and 10th terms in this sequence?
2. Can this sequence be expressed as a mathematical formula?
3. How does this sequence compare to a geometric progression?
4. What is the sum of the first 10 terms of this sequence?
5. How does the pattern of subtraction influence the convergence of the sequence?

**Tip:** When dealing with sequences, looking at differences between consecutive terms can often reveal the underlying pattern.

Explore the sequence of fractions: 1/2, 1/2, 3/8, 1/4, 5/32. Understand the pattern of decreasing fractions and calculate the 6th, 7th, and 8th terms step-by-step. Suitable for Grades 6-8 students learning about sequences and fractions.

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