What will come in place of question mark (?) in the given numbers series ?
4 11 24 44 72 ?

Options

A. 121
B. 113
C. 109
D. 118

Answer

To solve the number series problem: 4, 11, 24, 44, 72, ?, we will analyze the differences between consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **Identify the given series**:
The series is: 4, 11, 24, 44, 72, ?

2. **Calculate the differences between consecutive terms**:
- Difference between 11 and 4:
\( 11 - 4 = 7 \)
- Difference between 24 and 11:
\( 24 - 11 = 13 \)
- Difference between 44 and 24:
\( 44 - 24 = 20 \)
- Difference between 72 and 44:
\( 72 - 44 = 28 \)

So, the differences are: 7, 13, 20, 28.

3. **Calculate the differences of the differences** (second differences):
- Difference between 13 and 7:
\( 13 - 7 = 6 \)
- Difference between 20 and 13:
\( 20 - 13 = 7 \)
- Difference between 28 and 20:
\( 28 - 20 = 8 \)

So, the second differences are: 6, 7, 8.

4. **Identify the pattern in the second differences**:
The second differences are increasing by 1 each time. Following this pattern, the next second difference should be:
\( 8 + 1 = 9 \).

5. **Calculate the next first difference**:
The last first difference was 28. Adding the next second difference (which we found to be 9):
\( 28 + 9 = 37 \).

6. **Calculate the next term in the series**:
Now, we add this new first difference (37) to the last term in the original series (72):
\( 72 + 37 = 109 \).

Thus, the number that will come in place of the question mark (?) is **109**.

### Final Answer:
The answer is **109**.