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Let's analyze the question and solve it. 

The problem is about finding the formula for the \( n \)-th term (\( U_n \)) of a geometric sequence. We are given a sequence:

\[ 2, 8, 32, 128, \dots \]

### Step-by-Step Solution:

1. **Identify the first term (\( a \)):**
   - From the sequence, the first term \( a = 2 \).

2. **Find the common ratio (\( r \)):**
   - To find the common ratio, divide the second term by the first term:
     \[
     r = \frac{8}{2} = 4
     \]

3. **General formula for the \( n \)-th term of a geometric sequence:**
   - The formula for the \( n \)-th term of a geometric sequence is:
     \[
     U_n = a \cdot r^{n-1}
     \]
   - Substituting \( a = 2 \) and \( r = 4 \):
     \[
     U_n = 2 \cdot 4^{n-1}
     \]

### Final Answer:
The formula for the \( n \)-th term of the sequence is:
\[
U_n = 2 \cdot 4^{n-1}
\]

Would you like a further breakdown or have any questions about this solution?

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### Related Questions:
1. How would the formula change if the first term were different, for example \( a = 3 \)?
2. What happens to the \( n \)-th term formula if the common ratio is negative?
3. Can we derive the sum formula for the first \( n \) terms of this geometric sequence?
4. How would we find the term number \( n \) if we know the value of a specific term, say \( U_n = 512 \)?
5. What would be the \( n \)-th term formula if this was an arithmetic sequence instead of a geometric one?

### Tip:
When finding the common ratio in a geometric sequence, always ensure it’s consistent by dividing successive terms.

Tentukan rumus suku ke-n barisan geometri berikut: 2, 8, 32, 128, ...

Learn how to determine the formula for the n-th term of a geometric sequence with a starting term of 2 and a common ratio of 4. Includes a step-by-step solution using the formula Un = a * r^(n-1). Suitable for Grades 10-11.

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