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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: $2, -6, -54, 162$

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!