What should come in place of question mark (?) in the following questions.
1,3,6,?,18,29

Options

A. A)10
B. B)11
C. C)9
D. D)12

Answer

To solve the question of finding the missing term in the series 1, 3, 6, ?, 18, 29, we can follow these steps:

### Step 1: Identify the Pattern
We start by looking at the differences between consecutive terms in the series.

- The difference between the 1st term (1) and the 2nd term (3) is:
\[ 3 - 1 = 2 \]

- The difference between the 2nd term (3) and the 3rd term (6) is:
\[ 6 - 3 = 3 \]

- The difference between the 5th term (18) and the 6th term (29) is:
\[ 29 - 18 = 11 \]

Now we have the differences: 2, 3, ?, and 11.

### Step 2: Analyze the Differences
Next, we notice that the differences we have are:
- 2 (between 1 and 3)
- 3 (between 3 and 6)
- ? (between 6 and the missing term)
- 11 (between 18 and 29)

### Step 3: Find the Missing Difference
We can observe a pattern in the differences. The differences seem to be increasing. The next prime numbers after 2 and 3 are 5 and 7. If we follow the pattern of prime numbers, we can assume the missing difference is 5.

### Step 4: Calculate the Missing Term
Now we can calculate the missing term (let's call it K):
\[ K = 6 + 5 = 11 \]

### Step 5: Verify the Pattern
To ensure that our answer is correct, we can check the next difference:
- The difference from K (11) to the 5th term (18) is:
\[ 18 - 11 = 7 \]

Now we have:
- 2 (1 to 3)
- 3 (3 to 6)
- 5 (6 to 11)
- 7 (11 to 18)
- 11 (18 to 29)

This confirms that the differences are following the pattern of prime numbers (2, 3, 5, 7, 11).

### Conclusion
Thus, the missing term in the series is:
\[ \boxed{11} \]