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The image contains two geometric sequence problems written in Indonesian. Let's break them down and solve them step by step.

### Problem 1:
"Suku kedua dan suku kelima suatu barisan geometri berturut-turut adalah -6 dan 48. Suku keempat barisan geometri tersebut adalah…"

Translation: 
- The second term (suku kedua) and the fifth term (suku kelima) of a geometric sequence are -6 and 48, respectively. Find the fourth term of the sequence.

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

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

Using the formula for each term:
1. For the second term: \(a_2 = a_1 \cdot r = -6\),
   \[
   a_1 \cdot r = -6 \quad (1)
   \]
2. For the fifth term: \(a_5 = a_1 \cdot r^4 = 48\),
   \[
   a_1 \cdot r^4 = 48 \quad (2)
   \]

Now, divide equation (2) by equation (1):
\[
\frac{a_1 \cdot r^4}{a_1 \cdot r} = \frac{48}{-6}
\]
\[
r^3 = -8
\]
\[
r = -2
\]

Substitute \(r = -2\) into equation (1):
\[
a_1 \cdot (-2) = -6
\]
\[
a_1 = 3
\]

Now, to find the fourth term (\(a_4\)):
\[
a_4 = a_1 \cdot r^3 = 3 \cdot (-2)^3 = 3 \cdot (-8) = -24
\]

So, the fourth term is **-24**.

---

### Problem 2:
"Suku pertama dan rasio suatu barisan geometri berturut-turut adalah 2 dan 3. Jika jumlah n suku pertama deret tersebut adalah 80, tentukan banyak suku dari barisan tersebut."

Translation:
- The first term of a geometric sequence is 2, and the common ratio is 3. If the sum of the first n terms is 80, determine how many terms (n) are in the sequence.

### Solution:
The sum of the first n terms in a geometric sequence is given by:
\[
S_n = a_1 \cdot \frac{r^n - 1}{r - 1}
\]
where:
- \(S_n\) is the sum of the first n terms,
- \(a_1 = 2\) is the first term,
- \(r = 3\) is the common ratio.

We are given that \(S_n = 80\). Substituting the known values:
\[
80 = 2 \cdot \frac{3^n - 1}{3 - 1}
\]
\[
80 = 2 \cdot \frac{3^n - 1}{2}
\]
\[
80 = 3^n - 1
\]
\[
81 = 3^n
\]
\[
3^n = 81
\]

Since \(81 = 3^4\), we have:
\[
n = 4
\]

Thus, the number of terms (n) is **4**.

---

Would you like more details on any of these solutions or have further questions?

### Relative Questions:
1. How do you find the first term of a geometric sequence if given other terms?
2. What is the significance of the common ratio in a geometric sequence?
3. Can geometric sequences have a common ratio that is a fraction?
4. How can the sum formula for geometric sequences be applied to find missing terms?
5. What happens if the common ratio in a geometric series is negative?

### Tip:
In geometric sequences, knowing just two terms (that are far apart) can help you determine both the first term and the common ratio, allowing you to solve for any other terms.

Suku kedua dan suku kelima suatu barisan geometri berturut-turut adalah -6 dan 48. Suku keempat barisan geometri tersebut adalah...; Suku pertama dan rasio suatu barisan geometri berturut-turut adalah 2 dan 3. Jika jumlah n suku pertama deret tersebut adalah 80, tentukan banyak suku dari barisan tersebut.

Learn how to solve geometric sequence problems, including finding missing terms and determining the number of terms from a series sum. Problems involve second and fifth terms being given as -6 and 48, and a geometric series with a first term of 2 and a common ratio of 3. Suitable for Grades 10-12.

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