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.
`{:("2","6","16","38","84","178"),("3","A","B","C","D","E"):}`
What will come in place of D?

Options

A. 92
B. 88
C. 98
D. 100

Explanation

To solve the problem, we need to identify the pattern in the first series and apply it to the second series. Let's break it down step by step.

### Step 1: Analyze the first series
The first series is:
\[ 2, 6, 16, 38, 84, 178 \]

1. **From 2 to 6**:
- Multiply 2 by 2 to get 4, then add 2:
\[ 2 \times 2 + 2 = 4 + 2 = 6 \]

2. **From 6 to 16**:
- Multiply 6 by 2 to get 12, then add 4:
\[ 6 \times 2 + 4 = 12 + 4 = 16 \]

3. **From 16 to 38**:
- Multiply 16 by 2 to get 32, then add 6:
\[ 16 \times 2 + 6 = 32 + 6 = 38 \]

4. **From 38 to 84**:
- Multiply 38 by 2 to get 76, then add 8:
\[ 38 \times 2 + 8 = 76 + 8 = 84 \]

5. **From 84 to 178**:
- Multiply 84 by 2 to get 168, then add 10:
\[ 84 \times 2 + 10 = 168 + 10 = 178 \]

### Step 2: Identify the pattern
The pattern involves multiplying the previous term by 2 and then adding an increasing even number (2, 4, 6, 8, 10).

### Step 3: Apply the pattern to the second series
The second series starts with:
\[ 3, A, B, C, D, E \]

1. **Finding A**:
- Multiply 3 by 2 and add 2:
\[ 3 \times 2 + 2 = 6 + 2 = 8 \]
- So, \( A = 8 \)

2. **Finding B**:
- Multiply 8 by 2 and add 4:
\[ 8 \times 2 + 4 = 16 + 4 = 20 \]
- So, \( B = 20 \)

3. **Finding C**:
- Multiply 20 by 2 and add 6:
\[ 20 \times 2 + 6 = 40 + 6 = 46 \]
- So, \( C = 46 \)

4. **Finding D**:
- Multiply 46 by 2 and add 8:
\[ 46 \times 2 + 8 = 92 + 8 = 100 \]
- So, \( D = 100 \)

### Step 4: Conclusion
The value that comes in place of D is:
\[ \boxed{100} \]