Find the missing term in the following numbers series:
130,154,186,?,274,330

Options

A. A)216
B. B)220
C. C)240
D. D)226

Answer

To find the missing term in the number series: 130, 154, 186, ?, 274, 330, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given series**:
The series is 130, 154, 186, ?, 274, 330.

2. **Calculate the differences between consecutive terms**:
- Difference between 154 and 130:
\( 154 - 130 = 24 \)
- Difference between 186 and 154:
\( 186 - 154 = 32 \)
- Difference between 274 and 186:
\( 274 - 186 = ? \) (we will find this later)
- Difference between 330 and 274:
\( 330 - 274 = 56 \)

3. **List the differences**:
The differences we have so far are:
- 24 (from 130 to 154)
- 32 (from 154 to 186)
- ? (from 186 to k)
- 56 (from 274 to 330)

4. **Look for a pattern in the differences**:
The differences are:
- 24, 32, ?, 56
We can see that the difference from 24 to 32 is 8. If we continue this pattern:
- Next difference should be \( 32 + 8 = 40 \)
- The difference after that should be \( 40 + 8 = 48 \) (but this is not needed for our calculation)

5. **Calculate the missing term k**:
Now, we can use the difference of 40 to find k:
- From 186 to k:
\( k = 186 + 40 = 226 \)

6. **Verify the next difference**:
Now, let's check the difference from k (226) to 274:
- \( 274 - 226 = 48 \) (which fits our pattern)

### Conclusion:
The missing term in the series is **226**.