4 10 33 136 ? 4116

Options

A. 822
B. 534
C. 685
D. 745

Explanation

To solve the series 4, 10, 33, 136, ?, 4116, we will analyze the pattern in the series step by step.

### Step-by-step Solution:

1. **Identify the Pattern:**
- The series starts with 4, 10, 33, and 136. We need to find the missing number before 4116.

2. **Calculate the Transition from 4 to 10:**
- From 4 to 10:
\[ 4 \times 2 + 2 = 8 + 2 = 10 \]

3. **Calculate the Transition from 10 to 33:**
- From 10 to 33:
\[ 10 \times 3 + 3 = 30 + 3 = 33 \]

4. **Calculate the Transition from 33 to 136:**
- From 33 to 136:
\[ 33 \times 4 + 4 = 132 + 4 = 136 \]

5. **Calculate the Next Number in the Series:**
- Now, we will find the next number after 136:
\[ 136 \times 5 + 5 = 680 + 5 = 685 \]

6. **Verify the Next Transition to 4116:**
- Finally, we check if 685 leads correctly to 4116:
\[ 685 \times 6 + 6 = 4110 + 6 = 4116 \]

Thus, the missing number in the series is **685**.