10400 2600 650 ? 40.625 10.15625 2.5390625

Options

A. 175.5
B. 162.5
C. 154.75
D. 156.25

Explanation

To solve the series: 10400, 2600, 650, ?, 40.625, 10.15625, 2.5390625, we need to identify the pattern in the numbers.

### Step-by-Step Solution:

1. **Identify the Pattern**:
We observe that the numbers are decreasing. To find the missing number, we can check if there's a consistent division factor between consecutive terms.

2. **Divide the First Two Terms**:
- Divide 10400 by 2600:
\[ \frac{10400}{2600} = 4 \]
This indicates that the second term is 4 times smaller than the first term.

3. **Divide the Next Two Terms**:
- Divide 2600 by 650:
\[ \frac{2600}{650} = 4 \]
This confirms that the third term is also 4 times smaller than the second term.

4. **Find the Missing Term**:
- We can assume the missing term (let's call it \( x \)) follows the same pattern. So, we divide 650 by \( x \):
\[ \frac{650}{x} = 4 \implies x = \frac{650}{4} = 162.5 \]

5. **Verify the Next Terms**:
- Now, let's check if the next terms follow the same pattern:
- Divide 162.5 by 40.625:
\[ \frac{162.5}{40.625} = 4 \]
- Divide 40.625 by 10.15625:
\[ \frac{40.625}{10.15625} = 4 \]
- Divide 10.15625 by 2.5390625:
\[ \frac{10.15625}{2.5390625} = 4 \]

6. **Conclusion**:
Since all divisions confirm the pattern of dividing by 4, the missing term is indeed 162.5.

### Final Answer:
The missing number in the series is **162.5**.