https://file.aiquickdraw.com/mathbot/file/1725438865730vxj87hfx.jpg

The image contains five geometric sequences with missing terms that need to be identified. Let's analyze each sequence and find the missing terms.

### Problem Analysis and Solution:

1. **Sequence 1**: \( \_, 32, 16, 8 \)
   - To find the missing term, determine the common ratio:
     \[
     \text{Common ratio} = \frac{16}{32} = \frac{1}{2}
     \]
   - So, the sequence is multiplying each term by \(\frac{1}{2}\). To find the first term:
     \[
     32 \times \frac{1}{\frac{1}{2}} = 64
     \]
   - The missing term is **64**.

2. **Sequence 2**: \( 100, 50, 25, \_ \)
   - Common ratio:
     \[
     \frac{50}{100} = \frac{1}{2}
     \]
   - Continuing the pattern:
     \[
     25 \times \frac{1}{2} = 12.5
     \]
   - The missing term is **12.5**.

3. **Sequence 3**: \( -2, \_, -8, -32 \)
   - Common ratio:
     \[
     \frac{-8}{-2} = 4
     \]
   - To find the second term:
     \[
     -2 \times 4 = -8
     \]
   - The missing term is **-8**.

4. **Sequence 4**: \( \_, -16, -64, -256 \)
   - Common ratio:
     \[
     \frac{-64}{-16} = 4
     \]
   - To find the first term:
     \[
     -16 \times 4 = -4
     \]
   - The missing term is **4**.

5. **Sequence 5**: \( \frac{1}{3}, \frac{2}{5}, 2, 3 \)
   - Common ratio:
     \[
     2
     \]
   - To find the common ratio:
     \[
     \frac{-1}{-2} = 1
     \]
   - The missing term is **3**.

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Identify the value of the missing term in each geometric sequence.

This problem involves identifying the missing terms in various geometric sequences. The solution covers the calculation of the common ratio and how to apply it to find unknown terms. Suitable for students in Grades 6-8.

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