What value will come in place of question mark (?) in the questions given below?
`17, 27, 49, 83, 129, ?`

Options

A. 187
B. 185
C. 180
D. 182

Answer

To find the missing value in the sequence `17, 27, 49, 83, 129, ?`, we will look for a pattern in the differences between the consecutive numbers.

### Step-by-Step Solution:

1. **Identify the sequence**: The given sequence is `17, 27, 49, 83, 129`.

2. **Calculate the differences between consecutive numbers**:
- Difference between 27 and 17:
\[ 27 - 17 = 10 \]
- Difference between 49 and 27:
\[ 49 - 27 = 22 \]
- Difference between 83 and 49:
\[ 83 - 49 = 34 \]
- Difference between 129 and 83:
\[ 129 - 83 = 46 \]

So, the differences are: `10, 22, 34, 46`.

3. **Calculate the differences of the differences**:
- Difference between 22 and 10:
\[ 22 - 10 = 12 \]
- Difference between 34 and 22:
\[ 34 - 22 = 12 \]
- Difference between 46 and 34:
\[ 46 - 34 = 12 \]

The second level differences are constant: `12`.

4. **Predict the next difference**: Since the second level differences are constant at `12`, we can predict the next difference in the first level:
- Next difference = Last difference (46) + 12:
\[ 46 + 12 = 58 \]

5. **Calculate the next number in the sequence**:
- Add the predicted difference to the last number in the sequence:
\[ 129 + 58 = 187 \]

Thus, the missing value in the sequence is **187**.

### Final Answer:
The value that will come in place of question mark (?) is **187**.