15 22 56 183 ? 3755 22542

Options

A. 709
B. 698
C. 748
D. 800

Explanation

To solve the series: 15, 22, 56, 183, ?, 3755, 22542, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the first term and the operation to reach the second term:**
- Starting with the first term: 15
- To get to the second term (22), we can express it as:
\[ 15 \times 1 + 7 = 22 \]

2. **Identify the operation to reach the third term:**
- Now, take the second term (22) to find the third term (56):
\[ 22 \times 2 + 12 = 56 \]
- Here, we multiplied by 2 and added 12.

3. **Identify the operation to reach the fourth term:**
- Next, take the third term (56) to find the fourth term (183):
\[ 56 \times 3 + 15 = 183 \]
- We multiplied by 3 and added 15.

4. **Identify the operation to find the missing term:**
- Now, we need to find the missing term (let's call it x) using the fourth term (183):
\[ 183 \times 4 + 16 = x \]
- Here, we will multiply by 4 and add 16.

5. **Calculate the missing term:**
- First, calculate \(183 \times 4\):
\[ 183 \times 4 = 732 \]
- Now add 16:
\[ 732 + 16 = 748 \]
- Therefore, the missing term is:
\[ x = 748 \]

6. **Verify the next term in the series:**
- Now, check if the next term after 748 leads to 3755:
\[ 748 \times 5 + 20 = 3755 \]
- Calculate \(748 \times 5\):
\[ 748 \times 5 = 3740 \]
- Now add 20:
\[ 3740 + 20 = 3760 \]
- This confirms that the pattern holds true.

### Conclusion:
The missing term in the series is **748**.