The image shows a problem asking to find the indicated terms of geometric sequences. Let's solve each one.

1. $A_{10}$ of $3, 12, 48, \dots$

This is a geometric sequence with:

• First term $a = 3$
• Common ratio $r = \frac{12}{3} = 4$

The formula for the $n$-th term of a geometric sequence is: $A_n = a \cdot r^{n-1}$

For $A_{10}$: $A_{10} = 3 \cdot 4^{9}$

2. $A_4$ of $4, 12, 36, \dots$

This is a geometric sequence with:

• First term $a = 4$
• Common ratio $r = \frac{12}{4} = 3$

For $A_4$: $A_4 = 4 \cdot 3^{3}$

3. $A_{10}$ of $16,384, 4,096, 1,024, \dots$

This is a geometric sequence with:

• First term $a = 16,384$
• Common ratio $r = \frac{4,096}{16,384} = \frac{1}{4}$

For $A_{10}$: $A_{10} = 16,384 \cdot \left(\frac{1}{4}\right)^{9}$

4. $A_{10}$ of $3, 3\sqrt{5}, 15, 15\sqrt{5}, \dots$

This sequence has:

• First term $a = 3$
• Common ratio $r = \frac{3\sqrt{5}}{3} = \sqrt{5}$

For $A_{10}$: $A_{10} = 3 \cdot (\sqrt{5})^9$

I'll compute these values for you now.Here are the results for each geometric sequence:

1. $A_{10}$ of the sequence $3, 12, 48, \dots$ is 786,432.
2. $A_4$ of the sequence $4, 12, 36, \dots$ is 108.
3. $A_{10}$ of the sequence $16,384, 4,096, 1,024, \dots$ is 0.0625.
4. $A_{10}$ of the sequence $3, 3\sqrt{5}, 15, 15\sqrt{5}, \dots$ is approximately 4192.63.

Would you like more details or have any further questions? Here are five related questions you might consider:

1. How can the formula for a geometric sequence be derived?
2. What are the differences between arithmetic and geometric sequences?
3. How does the common ratio affect the growth or decay of a geometric sequence?
4. Can a geometric sequence have a common ratio of 1? What happens in this case?
5. How do you determine the sum of the first $n$ terms of a geometric sequence?

Tip: In a geometric sequence, if the common ratio is between 0 and 1, the terms decrease and approach zero.