121 138 159 184 213 ?

Options

A. 238
B. 252
C. 234
D. 246

Explanation

To find the missing number in the series: 121, 138, 159, 184, 213, ?, we will analyze the differences between consecutive terms.

### Step-by-step solution:

1. **Identify the series**: The series given is 121, 138, 159, 184, 213, ?.

2. **Calculate the differences between consecutive terms**:
- Difference between 138 and 121:
\[ 138 - 121 = 17 \]
- Difference between 159 and 138:
\[ 159 - 138 = 21 \]
- Difference between 184 and 159:
\[ 184 - 159 = 25 \]
- Difference between 213 and 184:
\[ 213 - 184 = 29 \]

3. **List the differences**:
- The differences we calculated are: 17, 21, 25, 29.

4. **Identify the pattern in the differences**:
- The differences are increasing.
- The difference between the first two differences (21 - 17) is 4.
- The difference between the next two differences (25 - 21) is also 4.
- The difference between the last two differences (29 - 25) is again 4.

5. **Continue the pattern**:
- The next difference should be:
\[ 29 + 4 = 33 \]

6. **Calculate the missing number**:
- Add this difference (33) to the last known term (213):
\[ 213 + 33 = 246 \]

7. **Conclusion**:
- The missing number in the series is **246**.