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The image contains various problems related to geometric sequences. Let me extract and solve them one by one.

### Problem 1: Determine if the sequence is geometric. If it is, find the common ratio.

- \( 11, 22, 44, 88, \ldots \)
  - This sequence has a constant ratio between consecutive terms:
  \[
  \frac{22}{11} = 2, \quad \frac{44}{22} = 2, \quad \frac{88}{44} = 2
  \]
  The sequence is geometric with a common ratio \( r = 2 \).

- \( 3, -6, 12, -24, \ldots \)
  - Checking the ratio:
  \[
  \frac{-6}{3} = -2, \quad \frac{12}{-6} = -2, \quad \frac{-24}{12} = -2
  \]
  The sequence is geometric with a common ratio \( r = -2 \).

### Problem 2: Find the explicit formula for the geometric sequence.

- Given \( a_1 = 4 \) and \( r = 3 \), the general formula for a geometric sequence is:
  \[
  a_n = a_1 \cdot r^{n-1} = 4 \cdot 3^{n-1}
  \]

### Problem 3: Find the first five terms and the sixth term.

- Using the formula \( a_n = 4 \cdot 3^{n-1} \), let's compute:
  \[
  a_1 = 4, \quad a_2 = 4 \cdot 3 = 12, \quad a_3 = 4 \cdot 9 = 36, \quad a_4 = 4 \cdot 27 = 108, \quad a_5 = 4 \cdot 81 = 324
  \]
  The first five terms are \( 4, 12, 36, 108, 324 \).

Do you want me to solve the remaining problems? Here are some follow-up questions:

1. What is the common ratio for the sequence \( 5, 10, 20, 40, \ldots \)?
2. How do you derive the explicit formula for any geometric sequence?
3. What is the significance of the first term in a geometric sequence?
4. Can a geometric sequence have a common ratio of 1? What does that imply?
5. How does a negative common ratio affect the terms of a geometric sequence?

**Tip**: Always verify the ratio between terms to confirm if a sequence is geometric.

Geometric sequences with various tasks such as finding the common ratio, deriving explicit formulas, and calculating terms.

Learn how to solve problems related to geometric sequences, including finding the common ratio, deriving explicit formulas, and calculating sequence terms. This lesson covers key concepts such as the common ratio and the general term formula, suitable for high school students in Grades 9-11.

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