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","12","30","66","138","282"),("7","A","B","C","D","E"):}`
What will come in place of B?

Options

A. 36
B. 70
C. 46
D. 62

Explanation

To solve the problem, we need to identify the pattern in the first series and then apply that pattern to the second series to find the value of B.

### Step-by-Step Solution:

1. **Identify the Pattern in the First Series:**
The first series is: 3, 12, 30, 66, 138, 282.
- To find the relationship, we can observe how each number is derived from the previous one.
- Start with 3:
- \(3 \times 2 = 6\) and \(6 + 6 = 12\)
- Next, from 12:
- \(12 \times 2 = 24\) and \(24 + 6 = 30\)
- Next, from 30:
- \(30 \times 2 = 60\) and \(60 + 6 = 66\)
- Next, from 66:
- \(66 \times 2 = 132\) and \(132 + 6 = 138\)
- Next, from 138:
- \(138 \times 2 = 276\) and \(276 + 6 = 282\)

The pattern observed is:
\[ \text{Next term} = (\text{Current term} \times 2) + 6 \]

2. **Apply the Pattern to the Second Series:**
The second series starts with 7 and is represented as: 7, A, B, C, D, E.
- First, we need to find A:
- \(A = 7 \times 2 + 6 = 14 + 6 = 20\)
- Now we have: 7, 20, B, C, D, E.
- Next, we find B:
- \(B = 20 \times 2 + 6 = 40 + 6 = 46\)

3. **Conclusion:**
The value that comes in place of B is 46.

### Final Answer:
B = 46