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### Problem 20:
In a geometric sequence, the common ratio \( r \) is defined as the fixed number multiplied by each term after the first term.

- **Option A**: Correct! This is the best description of the common ratio. Each term is multiplied by \( r \) to get the next.

### Problem 21:
We need to find the next two terms in the geometric sequence: \( 16, 128, \_\_, \_\_, 65536, \dots \).

- The ratio \( r \) is found by dividing \( 128 \) by \( 16 \), giving \( r = 8 \).
- The third term = \( 128 \times 8 = 1024 \).
- The fourth term = \( 1024 \times 8 = 8192 \).

Thus, the next two terms are **1024** and **8192** (Answer: **C**).

Would you like more explanations from the other problems?

Here are some related questions to deepen your understanding:
1. What is the general formula for the \( n \)-th term of a geometric sequence?
2. How do you find the common ratio in a geometric sequence if you are given multiple terms?
3. Can a geometric sequence have negative terms?
4. What is the difference between geometric and arithmetic sequences?
5. How do you find the sum of an infinite geometric series?

**Tip:** In a geometric sequence, multiplying by the common ratio repeatedly will eventually yield larger and larger terms if \( r > 1 \).

In a geometric sequence, which of the following best describes the common ratio 'r'?

Learn how the common ratio 'r' is used in geometric sequences. This problem explains the concept of the common ratio with examples and step-by-step solutions. Suitable for high school students.

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