1, 3, 3, 6, 7, 9, …. 12, 21.

Options

A. 10
B. 11
C. 12
D. 13

Explanation

To solve the series completion problem, we will analyze the given series step by step.

The series provided is: 1, 3, 3, 6, 7, 9, …, 12, 21.

### Step 1: Identify the two separate sequences
First, we can see that the series can be divided into two interleaved sequences:
- Sequence 1: 1, 3, 6, 9, 12
- Sequence 2: 3, 7, ?, 21

### Step 2: Analyze Sequence 1
Let's analyze the first sequence:
1, 3, 6, 9, 12.

To find the pattern, we can look at the differences between consecutive terms:
- 3 - 1 = 2
- 6 - 3 = 3
- 9 - 6 = 3
- 12 - 9 = 3

The first term increases by 2, and the subsequent terms increase by 3. Thus, the pattern for Sequence 1 is:
- Start with 1, add 2, then add 3 repeatedly.

### Step 3: Analyze Sequence 2
Now, let's analyze the second sequence:
3, 7, ?, 21.

We will also look at the differences here:
- 7 - 3 = 4
- ? - 7 = ?
- 21 - ? = ?

To find the missing term, we can assume that the pattern continues with increasing differences. The first difference is 4.

### Step 4: Find the missing term in Sequence 2
If we assume the next difference after 4 is 6 (increasing by 2), we can calculate:
- The next term after 7 would be 7 + 6 = 13.

Now, let's check if this fits with the next term:
- The difference between 21 and 13 should be 8 (which is also increasing by 2).
- 21 - 13 = 8.

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

### Final Answer
The missing number is **13**.