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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.

Solve for the indicated term of each geometric sequence below: A10 of 3, 12, 48,...; A4 of 4, 12, 36,...; A10 of 16,384, 4,096, 1,024,...; A10 of 3, 3√5, 15, 15√5,...

Learn how to solve geometric sequences for the 10th term. This example includes sequences like 3, 12, 48,... and provides detailed step-by-step solutions using the geometric sequence formula. Suitable for high school students.

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