What will come in the place of question mark (?) in the following number sereis:
11,?,16,21,29,41

Options

A. A)12
B. B)14
C. C)15
D. D)13

Answer

To find the missing term in the number series: 11, ?, 16, 21, 29, 41, we will analyze the pattern of differences between the terms.

### Step 1: Identify the known terms
The series is:
- 1st term: 11
- 2nd term: ?
- 3rd term: 16
- 4th term: 21
- 5th term: 29
- 6th term: 41

### Step 2: Calculate the differences between consecutive known terms
We will calculate the differences between the known terms:
- Difference between 16 and 21: \(21 - 16 = 5\)
- Difference between 21 and 29: \(29 - 21 = 8\)
- Difference between 29 and 41: \(41 - 29 = 12\)

So, the differences we have so far are:
- From 16 to 21: 5
- From 21 to 29: 8
- From 29 to 41: 12

### Step 3: Identify the pattern in the differences
Now, let's look at the differences:
- The difference from 5 to 8 is \(8 - 5 = 3\)
- The difference from 8 to 12 is \(12 - 8 = 4\)

We see that the differences themselves are increasing:
- First difference: 5
- Second difference: 8 (which is 5 + 3)
- Third difference: 12 (which is 8 + 4)

### Step 4: Establish the pattern for the missing term
To find the missing term, we need to find the difference before 5. If we follow the pattern, we can assume the difference before 5 would be \(5 - 2 = 3\).

### Step 5: Calculate the missing term
Now we can calculate the missing term (let's denote it as K):
- Since the difference before 16 (the 3rd term) is 3, we can calculate K:
\[ K = 16 - 3 = 13 \]

### Conclusion
Thus, the missing term in the series is **13**.

### Final Answer
The answer is **13**.