7 8 16 43 ? 232

Options

A. 204
B. 107
C. 119
D. 89

Explanation

To solve the series 7, 8, 16, 43, ?, 232, we need to identify the pattern in the differences between the numbers.

### Step-by-Step Solution:

1. **Identify the first number in the series**: The series starts with 7.

2. **Calculate the difference between the first two numbers**:
- \(8 - 7 = 1\)

3. **Calculate the difference between the second and third numbers**:
- \(16 - 8 = 8\)

4. **Calculate the difference between the third and fourth numbers**:
- \(43 - 16 = 27\)

5. **List the differences found**:
- The differences are: 1, 8, 27.

6. **Recognize the pattern in the differences**:
- The differences can be expressed as cubes:
- \(1 = 1^3\)
- \(8 = 2^3\)
- \(27 = 3^3\)

7. **Predict the next difference**:
- Following the pattern, the next difference should be \(4^3 = 64\).

8. **Calculate the next number in the series**:
- Add the predicted difference to the last known number:
- \(43 + 64 = 107\)

9. **Verify the next difference**:
- Now, calculate the difference between the last number (107) and the final number in the series (232):
- \(232 - 107 = 125\)
- Check if this difference is a cube:
- \(125 = 5^3\)

10. **Conclusion**:
- The number that fits in the series is 107.

### Final Answer:
The missing number in the series is **107**.