The problem asks to extend the sequence $8, 16, 32, \dots$ using the rule "Multiply by 2." Let's solve this:

1. Start with the given sequence: $8, 16, 32$

2. Multiply the last number $32$ by $2$: $32 \times 2 = 64$

3. Multiply $64$ by $2$ to find the next number: $64 \times 2 = 128$

Thus, the next two numbers in the sequence are 64 and 128.

Correct answers:

• First box: $\mathbf{C} \, 64$
• Second box: $\mathbf{B} \, 128$

Would you like additional details or explanations?

Here are 5 related questions to explore further:

1. What is a geometric sequence, and how is it different from an arithmetic sequence?
2. How can we write the formula for the $n$-th term of this sequence?
3. If the sequence starts at 4 instead of 8, what will the next numbers be?
4. How would the pattern change if the rule was "Add 8" instead of "Multiply by 2"?
5. Can you identify any applications of such exponential growth patterns in real life?

Tip: When dealing with patterns, always verify the rule consistently across all elements of the sequence.