What will come in place of question mark(?) in the given number series.
16 19 24 33 50 ?

Options

A. 83
B. 66
C. 99
D. 74

Answer

To solve the number series: 16, 19, 24, 33, 50, ?, we need to identify the pattern in the differences between the consecutive numbers.

1. **Calculate the differences between consecutive terms:**
- 19 - 16 = 3
- 24 - 19 = 5
- 33 - 24 = 9
- 50 - 33 = 17

So the differences are: 3, 5, 9, 17.

2. **Identify the pattern in the differences:**
- The differences themselves are: 3, 5, 9, 17.
- To find the next difference, we can look at the differences between the differences:
- 5 - 3 = 2
- 9 - 5 = 4
- 17 - 9 = 8

So the second-level differences are: 2, 4, 8.

3. **Identify the pattern in the second-level differences:**
- The second-level differences are: 2, 4, 8.
- These are powers of 2: 2^1, 2^2, 2^3.
- The next term in this sequence would be 2^4 = 16.

4. **Calculate the next difference:**
- The last difference we calculated was 17.
- If we add the next second-level difference (16) to the last difference (17), we get:
- 17 + 16 = 33.

5. **Calculate the next term in the original series:**
- The last term in the series is 50.
- We add the new difference (33) to this term:
- 50 + 33 = 83.

Thus, the number that comes in place of the question mark (?) is **83**.