What should come in place of the question mark (?) in the following number series ?
`"4 7 11 18 29 ? 76"`

Options

A. 64
B. 38
C. 52
D. 47

Answer

To solve the number series: 4, 7, 11, 18, 29, ?, 76, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the differences between consecutive terms**:
- 7 - 4 = 3
- 11 - 7 = 4
- 18 - 11 = 7
- 29 - 18 = 11

So, the differences are: 3, 4, 7, 11.

2. **Identify the differences of the differences**:
- 4 - 3 = 1
- 7 - 4 = 3
- 11 - 7 = 4

The second differences are: 1, 3, 4.

3. **Identify the pattern in the second differences**:
- The second differences do not form a simple arithmetic sequence, but we can see that the differences are increasing.

4. **Continue the pattern**:
- The next difference after 11 can be calculated by adding the last second difference (which is 4) to the last first difference (which is 11).
- So, the next difference = 11 + 4 = 15.

5. **Calculate the next term**:
- Now, add this new difference (15) to the last known term (29):
- 29 + 15 = 44.

6. **Calculate the next term**:
- Now, we need to find the next term before 76. The difference between the next term and 76 should also follow the pattern.
- The difference from 44 to 76 should be calculated:
- 76 - 44 = 32.

7. **Final series**:
- The complete series now looks like this: 4, 7, 11, 18, 29, 44, 76.

Thus, the value that should come in place of the question mark (?) is **44**.