what should come in place of question mark( ?) in the following number series ?
`0" "5" "18" "43" "84" "145 " "?`

Options

A. 220
B. 230
C. 260
D. 280

Answer

To solve the number series question, we need to identify the pattern in the sequence: `0, 5, 18, 43, 84, 145, ?`.

### Step-by-Step Solution:

1. **Identify the Differences**:
- First, we calculate the differences between consecutive terms in the series.
- \( 5 - 0 = 5 \)
- \( 18 - 5 = 13 \)
- \( 43 - 18 = 25 \)
- \( 84 - 43 = 41 \)
- \( 145 - 84 = 61 \)

So, the first differences are: `5, 13, 25, 41, 61`.

2. **Identify the Second Differences**:
- Next, we calculate the differences of the first differences.
- \( 13 - 5 = 8 \)
- \( 25 - 13 = 12 \)
- \( 41 - 25 = 16 \)
- \( 61 - 41 = 20 \)

So, the second differences are: `8, 12, 16, 20`.

3. **Identify the Third Differences**:
- Now, we calculate the differences of the second differences.
- \( 12 - 8 = 4 \)
- \( 16 - 12 = 4 \)
- \( 20 - 16 = 4 \)

The third differences are constant: `4`.

4. **Predict the Next Second Difference**:
- Since the third differences are constant, we can predict the next second difference.
- The next second difference would be \( 20 + 4 = 24 \).

5. **Predict the Next First Difference**:
- Now, we add this new second difference to the last first difference.
- \( 61 + 24 = 85 \).

6. **Predict the Next Term in the Series**:
- Finally, we add this new first difference to the last term in the original series.
- \( 145 + 85 = 230 \).

Thus, the term that should come in place of the question mark (?) is **230**.

### Final Answer:
The answer is **230**.