6, 17, 55, 196, 825, ?

Options

A. 4176
B. 4212
C. 4232
D. 4256

Explanation

To find the missing number in the series: 6, 17, 55, 196, 825, ?, we will analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the first two numbers (6 and 17)**:
- To go from 6 to 17, we can observe:
\[ 17 - 6 = 11 \]
- We can express this as:
\[ 6 \times 1 + 11 = 17 \]

2. **Identify the next two numbers (17 and 55)**:
- To go from 17 to 55, we first calculate:
\[ 55 - 17 = 38 \]
- We can express this as:
\[ 17 \times 2 + 21 = 55 \]

3. **Identify the next two numbers (55 and 196)**:
- To go from 55 to 196, we calculate:
\[ 196 - 55 = 141 \]
- We can express this as:
\[ 55 \times 3 + 31 = 196 \]

4. **Identify the next two numbers (196 and 825)**:
- To go from 196 to 825, we calculate:
\[ 825 - 196 = 629 \]
- We can express this as:
\[ 196 \times 4 + 41 = 825 \]

5. **Identify the next number after 825**:
- Following the pattern, we will multiply 825 by 5 and then add 51:
\[ 825 \times 5 + 51 \]
- First, calculate \(825 \times 5\):
\[ 825 \times 5 = 4125 \]
- Now, add 51:
\[ 4125 + 51 = 4176 \]

Thus, the missing number in the series is **4176**.