https://file.aiquickdraw.com/mathbot/file/17258823028583bv55p5f.jpg

Let's go through the geometric sequences shown in the image and solve for the next three terms for each one.

1. **Sequence 1**: \( 1, \frac{1}{2}, \frac{1}{4}, \ldots \)
   - To find the common ratio (\( r \)), divide the second term by the first:
     \[
     r = \frac{\frac{1}{2}}{1} = \frac{1}{2}
     \]
   - Now, multiply each term by \( \frac{1}{2} \) to get the next terms:
     \[
     \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
     \]
     \[
     \frac{1}{8} \times \frac{1}{2} = \frac{1}{16}
     \]
     \[
     \frac{1}{16} \times \frac{1}{2} = \frac{1}{32}
     \]
   - So, the next three terms are \( \frac{1}{8}, \frac{1}{16}, \frac{1}{32} \).

2. **Sequence 2**: \( 100, 20, 4, \ldots \)
   - Find the common ratio:
     \[
     r = \frac{20}{100} = \frac{1}{5}
     \]
   - Multiply the terms by \( \frac{1}{5} \):
     \[
     4 \times \frac{1}{5} = \frac{4}{5}
     \]
     \[
     \frac{4}{5} \times \frac{1}{5} = \frac{4}{25}
     \]
     \[
     \frac{4}{25} \times \frac{1}{5} = \frac{4}{125}
     \]
   - The next three terms are \( \frac{4}{5}, \frac{4}{25}, \frac{4}{125} \).

3. **Sequence 3**: \( \frac{8}{3}, \frac{4}{3}, \frac{2}{3}, \ldots \)
   - Find the common ratio:
     \[
     r = \frac{\frac{4}{3}}{\frac{8}{3}} = \frac{1}{2}
     \]
   - Multiply the terms by \( \frac{1}{2} \):
     \[
     \frac{2}{3} \times \frac{1}{2} = \frac{1}{3}
     \]
     \[
     \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}
     \]
     \[
     \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}
     \]
   - The next three terms are \( \frac{1}{3}, \frac{1}{6}, \frac{1}{12} \).

4. **Sequence 4**: \( -1, 2, -4, \ldots \)
   - Find the common ratio:
     \[
     r = \frac{2}{-1} = -2
     \]
   - Multiply the terms by \( -2 \):
     \[
     -4 \times (-2) = 8
     \]
     \[
     8 \times (-2) = -16
     \]
     \[
     -16 \times (-2) = 32
     \]
   - The next three terms are \( 8, -16, 32 \).

Would you like any more details on these solutions?

### Related Questions:
1. How do you find the common ratio in a geometric sequence?
2. What is the difference between geometric and arithmetic sequences?
3. How do you find the sum of a geometric series?
4. How do negative ratios affect the behavior of a geometric sequence?
5. How can you apply geometric sequences in real-life scenarios?

### Tip:
Always double-check the common ratio when multiplying to find the next terms—it ensures your sequence remains correct!

Find the next three terms in each geometric sequence from the provided set of sequences.

Learn how to find the next three terms in a geometric sequence. This guide covers geometric sequences, common ratio calculations, and how to multiply terms by the ratio to predict future values. Perfect for Grades 6-8 students.

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