What will come in place of question mark (? ) in the following number series ?
`13" "16 " "22" "33" "51" "?`

Options

A. 89
B. 78
C. 102
D. 69

Answer

To solve the number series question, we need to identify the pattern in the series: 13, 16, 22, 33, 51, ?

### Step-by-Step Solution:

1. **Identify the Series**:
The given series is 13, 16, 22, 33, 51.

2. **Calculate the Differences**:
- From 13 to 16: \( 16 - 13 = 3 \)
- From 16 to 22: \( 22 - 16 = 6 \)
- From 22 to 33: \( 33 - 22 = 11 \)
- From 33 to 51: \( 51 - 33 = 18 \)

So, the differences are: 3, 6, 11, 18.

3. **Find the Differences of the Differences**:
Now, let's find the differences between these differences:
- From 3 to 6: \( 6 - 3 = 3 \)
- From 6 to 11: \( 11 - 6 = 5 \)
- From 11 to 18: \( 18 - 11 = 7 \)

The second level of differences is: 3, 5, 7.

4. **Identify the Pattern in the Second Differences**:
The differences of the differences (3, 5, 7) are increasing by 2 each time:
- From 3 to 5: \( 5 - 3 = 2 \)
- From 5 to 7: \( 7 - 5 = 2 \)

This suggests that the next difference in this sequence will be \( 7 + 2 = 9 \).

5. **Calculate the Next Difference**:
Now, we add this new difference (9) to the last difference we calculated (18):
- Next difference: \( 18 + 9 = 27 \)

6. **Add the New Difference to the Last Term**:
Finally, we add this new difference (27) to the last term of the original series (51):
- \( 51 + 27 = 78 \)

Thus, the number that comes in place of the question mark (?) is **78**.

### Final Answer:
The answer is **78**.