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The problem is asking to find the common ratio (\(r\)) of a geometric sequence where the second term (\(a_2\)) is \(-6\) and the fifth term (\(a_5\)) is \(48\).

In a geometric sequence, the \(n\)-th term is given by the formula:
\[
a_n = a_1 \cdot r^{n-1}
\]
where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(r\) is the common ratio, and
- \(n\) is the position of the term.

We are given:
- \(a_2 = -6\),
- \(a_5 = 48\).

We can set up two equations:
1. \(a_2 = a_1 \cdot r^1 = -6\),
2. \(a_5 = a_1 \cdot r^4 = 48\).

### Step 1: Solve for \(a_1\) and \(r\)
From the first equation, \(a_1 \cdot r = -6\), so:
\[
a_1 = \frac{-6}{r}
\]

Substitute this into the second equation:
\[
\left(\frac{-6}{r}\right) \cdot r^4 = 48
\]
Simplify:
\[
-6 \cdot r^3 = 48
\]
\[
r^3 = \frac{48}{-6} = -8
\]

### Step 2: Solve for \(r\)
\[
r = \sqrt[3]{-8} = -2
\]

Thus, the common ratio of the geometric sequence is \(r = -2\).

Would you like more details on any step? Here are some related questions:

1. How do you derive the formula for the nth term of a geometric sequence?
2. What are the conditions for a geometric sequence to be convergent or divergent?
3. How would the process change if we had different terms given?
4. Can you explain why a negative ratio causes alternating terms?
5. How does the formula for geometric sequences apply to infinite series?

**Tip:** Always verify your result by substituting back into the original equations to ensure accuracy.

Diketahui barisan geometri dengan suku ke-2 = -6 dan suku ke-5 = 48. Berapakah rasio pada barisan tersebut?

Learn how to find the common ratio of a geometric sequence where the second term is -6 and the fifth term is 48. This problem involves applying the geometric sequence formula to solve for the ratio, suitable for high school students in Grades 10-12.

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