What should come in place of question mark (?) in the given number series ?
256 252 225 209 84 ?

Options

A. 48
B. 42
C. 44
D. 40

Answer

To solve the number series problem, we need to identify the pattern in the given numbers: 256, 252, 225, 209, 84, ?.

### Step-by-Step Solution:

1. **Identify the Series**:
The series given is: 256, 252, 225, 209, 84, ?.

2. **Calculate the Differences**:
- From 256 to 252:
\( 256 - 252 = 4 \)
- From 252 to 225:
\( 252 - 225 = 27 \)
- From 225 to 209:
\( 225 - 209 = 16 \)
- From 209 to 84:
\( 209 - 84 = 125 \)

So the differences are: 4, 27, 16, 125.

3. **Recognize the Pattern**:
- The differences can be expressed as:
- \( 4 = 2^2 \) (even number)
- \( 27 = 3^3 \) (odd number)
- \( 16 = 4^2 \) (even number)
- \( 125 = 5^3 \) (odd number)

This suggests a pattern where even indexed differences are squares and odd indexed differences are cubes.

4. **Determine the Next Difference**:
- Following the pattern, the next difference should be \( 6^2 = 36 \) (since 6 is the next even number).

5. **Calculate the Missing Number**:
- Now, we subtract this difference from the last number in the series:
\( 84 - 36 = 48 \).

6. **Conclusion**:
Therefore, the number that should come in place of the question mark (?) is **48**.

### Final Answer:
The answer is **48**.