What will come in place of question mark(?) in the given number series?
169 177 150 214 89 ?

Options

A. 305
B. 295
C. 280
D. 405

Answer

To solve the given number series: 169, 177, 150, 214, 89, ?, we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Sequence**:
The series is: 169, 177, 150, 214, 89, ?

2. **Calculate Differences**:
- From 169 to 177:
\[ 177 - 169 = 8 \]
- From 177 to 150:
\[ 150 - 177 = -27 \]
- From 150 to 214:
\[ 214 - 150 = 64 \]
- From 214 to 89:
\[ 89 - 214 = -125 \]

3. **List the Differences**:
The differences we calculated are:
\[ +8, -27, +64, -125 \]

4. **Recognize the Pattern**:
The differences can be expressed in terms of cubes:
- \(8 = 2^3\)
- \(-27 = -3^3\)
- \(64 = 4^3\)
- \(-125 = -5^3\)

5. **Predict the Next Difference**:
Following the pattern, the next difference should be:
- \(6^3 = 216\) (since we alternate between adding and subtracting)

6. **Calculate the Next Number**:
Since the last operation was subtraction, we will add the next difference:
\[ 89 + 216 = 305 \]

7. **Conclusion**:
The value that comes in place of the question mark (?) is **305**.

### Final Answer:
305