2 13 35 68 112 ?

Options

A. 173
B. 178
C. 163
D. 167

Explanation

To solve the series: 2, 13, 35, 68, 112, ?, we need to identify the pattern in the differences between the consecutive numbers.

### Step-by-Step Solution:

1. **Identify the Series**:
The given series is: 2, 13, 35, 68, 112.

2. **Calculate the Differences**:
We will find the difference between each pair of consecutive numbers:
- Difference between 13 and 2:
\( 13 - 2 = 11 \)
- Difference between 35 and 13:
\( 35 - 13 = 22 \)
- Difference between 68 and 35:
\( 68 - 35 = 33 \)
- Difference between 112 and 68:
\( 112 - 68 = 44 \)

So, the differences are: 11, 22, 33, 44.

3. **Identify the Pattern in Differences**:
The differences themselves form a series:
- 11, 22, 33, 44.
We can see that these differences increase by 11 each time.

4. **Predict the Next Difference**:
Following the pattern, the next difference should be:
\( 44 + 11 = 55 \).

5. **Calculate the Next Number**:
To find the next number in the original series, we add this next difference to the last number in the series:
\( 112 + 55 = 167 \).

6. **Conclusion**:
Therefore, the missing number in the series is **167**.

### Final Answer:
The next number in the series is **167**.