It looks like you've uploaded a math worksheet. I'll walk through a few of the problems step by step, starting with a selection. Let me know which ones you'd like a detailed explanation of!

For example, here’s how to solve some of the questions:

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 $r > 1$.