What should come in place of the question mark(?) in the following number series?
13 30 66 140 ? 592

Options

A. 210
B. 290
C. 428
D. 430

Answer

To solve the number series: 13, 30, 66, 140, ?, 592, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Differences**:
- First, let's find the differences between consecutive terms.
- 30 - 13 = 17
- 66 - 30 = 36
- 140 - 66 = 74

So, the differences are: 17, 36, 74.

2. **Identify the Differences of Differences**:
- Now, let's find the differences of these differences.
- 36 - 17 = 19
- 74 - 36 = 38

So, the second-level differences are: 19, 38.

3. **Identify the Pattern in Second-Level Differences**:
- Now, let's find the difference of the second-level differences.
- 38 - 19 = 19

The third-level difference is constant (19), suggesting that the second-level differences increase by 19 each time.

4. **Calculate the Next Second-Level Difference**:
- The next second-level difference would be 38 + 19 = 57.

5. **Calculate the Next First-Level Difference**:
- Now, add this new second-level difference to the last first-level difference:
- 74 + 57 = 131.

6. **Calculate the Missing Term**:
- Now, add this first-level difference to the last known term in the series:
- 140 + 131 = 271.

7. **Verify with the Next Term**:
- Finally, let's check if this fits with the next term (592).
- The difference between 592 and 271 should match the expected difference:
- 592 - 271 = 321.

8. **Final Check**:
- Now we can see if the differences continue to follow the pattern:
- The next difference after 271 should be 131 + 57 = 188.
- 271 + 188 = 459, and then 459 + 131 = 592, confirming our calculations.

Thus, the missing term in the series is **271**.

### Final Answer:
The number that should come in place of the question mark (?) is **271**.