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### Problem 5 (Geometric Sequence)
We need to complete each geometric sequence with the missing terms and determine the growth factor for each:

1. \( 4, 16, 64, \_\_, 1024 \)
   - Growth factor = 4 (since \( \frac{16}{4} = 4 \))
   - Missing term: \( 64 \times 4 = 256 \)
   - Sequence: \( 4, 16, 64, 256, 1024 \)

2. \( 3, 6, 12, \_\_, 48 \)
   - Growth factor = 2 (since \( \frac{6}{3} = 2 \))
   - Missing term: \( 12 \times 2 = 24 \)
   - Sequence: \( 3, 6, 12, 24, 48 \)

3. \( 2, \_\_, 10, 50, 250, 1250 \)
   - Growth factor = 5 (since \( \frac{10}{2} = 5 \))
   - Missing term: \( 2 \times 5 = 10 \)
   - Sequence: \( 2, 10, 50, 250, 1250 \)

4. \( -8, -2, \_\_, 0.5, -0.125 \)
   - Growth factor = -0.25 (since \( \frac{-2}{-8} = 0.25 \))
   - Missing term: \( -2 \times (-0.25) = 0.5 \)
   - Sequence: \( -8, -2, 0.5, -0.125 \)

5. \( 2, \_\_, -54, 162 \)
   - Growth factor = -3 (since \( \frac{-54}{2} = -3 \))
   - Missing term: \( 2 \times (-3) = -6 \)
   - Sequence: \( 2, -6, -54, 162 \)

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Would you like to see the solution to the arithmetic sequences, or do you have any further questions about these geometric sequences?

Here are 5 related questions for further practice:
1. How do you find the growth factor in a geometric sequence?
2. What is the formula for the \(n\)-th term in a geometric sequence?
3. Can a geometric sequence have a negative growth factor?
4. How do you distinguish between an arithmetic and a geometric sequence?
5. What happens to a geometric sequence when the growth factor is 1?

**Tip:** Always divide the second term by the first to identify the growth factor in a geometric sequence!

Complete each geometric sequence with the missing terms and find the growth factor for each.

Learn how to complete geometric sequences and find the growth factor. This problem involves calculating missing terms using geometric growth. Perfect for students in Grades 7-9.

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