What will come in place of the question mark (?) in the given number series?
257 129 65 33 17 ?

Options

A. 9
B. 5
C. 6
D. 8

Answer

To solve the number series: 257, 129, 65, 33, 17, ?, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is 257, 129, 65, 33, 17, ?.

2. **Calculate the Differences**:
- First difference: 257 - 129 = 128
- Second difference: 129 - 65 = 64
- Third difference: 65 - 33 = 32
- Fourth difference: 33 - 17 = 16

3. **Observe the Pattern in Differences**:
- The differences we calculated are: 128, 64, 32, 16.
- Notice that each difference is half of the previous difference:
- 128 / 2 = 64
- 64 / 2 = 32
- 32 / 2 = 16

4. **Continue the Pattern**:
- Following the pattern, the next difference should be half of 16, which is 8.

5. **Calculate the Next Number**:
- To find the missing number, subtract the next difference (8) from the last number in the series (17):
- 17 - 8 = 9

6. **Conclusion**: The number that will come in place of the question mark (?) is **9**.

### Final Answer:
The answer is **9**.