You are given two series in two rows. In the first row, a full series is given which follows a specific pattern. The second row has a series, similar to the first series but only first element of this series is produced followed by (A), (B), (C), (D) and (E) for the subsequent elements. You have to complete the series starting with a given number and answer the question that follows.
`{:("3","4","12","45","196","1005"),("5","A","B","C","D","E"):}`
What will come in place of D?

Options

A. 244
B. 236
C. 216
D. 224

Explanation

To solve the problem, we need to identify the pattern in the first series and then apply that pattern to the second series. Let's go through the steps:

### Step 1: Identify the Pattern in the First Series
The first series is: 3, 4, 12, 45, 196, 1005.

1. **From 3 to 4**:
- We multiply 3 by 1 and add \(1^2\):
\[ 3 \times 1 + 1^2 = 3 + 1 = 4 \]

2. **From 4 to 12**:
- We multiply 4 by 2 and add \(2^2\):
\[ 4 \times 2 + 2^2 = 8 + 4 = 12 \]

3. **From 12 to 45**:
- We multiply 12 by 3 and add \(3^2\):
\[ 12 \times 3 + 3^2 = 36 + 9 = 45 \]

4. **From 45 to 196**:
- We multiply 45 by 4 and add \(4^2\):
\[ 45 \times 4 + 4^2 = 180 + 16 = 196 \]

5. **From 196 to 1005**:
- We multiply 196 by 5 and add \(5^2\):
\[ 196 \times 5 + 5^2 = 980 + 25 = 1005 \]

### Step 2: Apply the Pattern to the Second Series
The second series starts with 5 and has the pattern A, B, C, D, E.

1. **Finding A**:
- We multiply 5 by 1 and add \(1^2\):
\[ 5 \times 1 + 1^2 = 5 + 1 = 6 \]

2. **Finding B**:
- We multiply 6 by 2 and add \(2^2\):
\[ 6 \times 2 + 2^2 = 12 + 4 = 16 \]

3. **Finding C**:
- We multiply 16 by 3 and add \(3^2\):
\[ 16 \times 3 + 3^2 = 48 + 9 = 57 \]

4. **Finding D**:
- We multiply 57 by 4 and add \(4^2\):
\[ 57 \times 4 + 4^2 = 228 + 16 = 244 \]

### Conclusion
Thus, the value that comes in place of D is **244**.