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To find the common ratio \( r \) of the geometric sequence, we can use the information given:

- The third term \( a_3 = -108 \)
- The eighth term \( a_8 = 26,244 \)

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

### Step 1: Set up equations
Using the third term:
\[
a \cdot r^{2} = -108
\]
Using the eighth term:
\[
a \cdot r^{7} = 26,244
\]

### Step 2: Divide the equations to eliminate \( a \)
Dividing the second equation by the first:
\[
\frac{a \cdot r^{7}}{a \cdot r^{2}} = \frac{26,244}{-108}
\]
This simplifies to:
\[
r^{5} = \frac{26,244}{-108}
\]

### Step 3: Calculate \( r^{5} \)
\[
r^{5} = -243
\]

### Step 4: Find \( r \) by taking the fifth root
The fifth root of \( -243 \) is \( -3 \).

### Answer
The common ratio \( r \) is \( \mathbf{-3} \).

Let me know if you'd like more details or have any questions! 

Here are some related questions to practice:

1. How would you find the first term of this sequence given the third term and common ratio?
2. What would the tenth term of this sequence be?
3. How do you determine if a sequence is geometric?
4. What is the formula to sum the first \( n \) terms of a geometric sequence?
5. How would the solution change if the eighth term were negative?

**Tip:** In a geometric sequence, dividing two consecutive terms gives the common ratio.

A geometric sequence has a third term of -108 and an eighth term of 26,244. What is the common ratio between sequence values?

Learn how to determine the common ratio in a geometric sequence given the third term as -108 and the eighth term as 26,244. This problem involves using the nth term formula of a geometric sequence, suitable for high school students.

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