45 57 81 117 165 ?

Options

A. 235
B. 215
C. 205
D. 225

Explanation

To find the next number in the series: 45, 57, 81, 117, 165, we will analyze the differences between consecutive terms.

### Step-by-Step Solution:

1. **Identify the series**:
The series given is: 45, 57, 81, 117, 165.

2. **Calculate the differences between consecutive terms**:
- Difference between 57 and 45:
\[ 57 - 45 = 12 \]
- Difference between 81 and 57:
\[ 81 - 57 = 24 \]
- Difference between 117 and 81:
\[ 117 - 81 = 36 \]
- Difference between 165 and 117:
\[ 165 - 117 = 48 \]

3. **List the differences**:
The differences we calculated are:
- 12, 24, 36, 48.

4. **Identify the pattern in the differences**:
- The differences themselves form a series: 12, 24, 36, 48.
- Notice that these differences increase by 12 each time:
- 24 - 12 = 12
- 36 - 24 = 12
- 48 - 36 = 12

5. **Predict the next difference**:
- Continuing the pattern, the next difference should be:
\[ 48 + 12 = 60 \]

6. **Add the next difference to the last term in the original series**:
- Now, add this difference to the last term (165):
\[ 165 + 60 = 225 \]

7. **Conclusion**:
- The next number in the series is **225**.

### Final Answer:
The required number is **225**.