17, 18, 38, 117, ?, 2365

Options

A. 450
B. 434
C. 530
D. 472

Explanation

To solve the series: 17, 18, 38, 117, ?, 2365, we will look for a pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The first number is 17.
- The second number is 18, which can be represented as:
\[ 17 \times 1 + 1 = 18 \]
- The third number is 38, which can be represented as:
\[ 18 \times 2 + 2 = 38 \]
- The fourth number is 117, which can be represented as:
\[ 38 \times 3 + 3 = 117 \]

2. **Finding the Next Number**:
- Following the established pattern, the next number should be calculated as:
\[ 117 \times 4 + 4 \]
- First, calculate \( 117 \times 4 \):
\[ 117 \times 4 = 468 \]
- Now, add 4:
\[ 468 + 4 = 472 \]

3. **Confirming the Last Number**:
- Now, we need to check if this number fits into the series leading to 2365:
\[ 472 \times 5 + 5 \]
- First, calculate \( 472 \times 5 \):
\[ 472 \times 5 = 2360 \]
- Now, add 5:
\[ 2360 + 5 = 2365 \]

4. **Conclusion**:
- The missing number in the series is **472**.

### Final Answer:
The missing number is **472**.