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.
`{:("7","13","29","53","113","217"),("5","A","B","C","D","E"):}`
What will come in place of E?

Options

A. 173
B. 171
C. 153
D. 151

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 break it down step by step.

### Step 1: Identify the pattern in the first series
The first series is:
7, 13, 29, 53, 113, 217.

1. **From 7 to 13**:
- Multiply 7 by 2: \(7 \times 2 = 14\).
- Subtract 1: \(14 - 1 = 13\).

2. **From 13 to 29**:
- Multiply 13 by 2: \(13 \times 2 = 26\).
- Add 3: \(26 + 3 = 29\).

3. **From 29 to 53**:
- Multiply 29 by 2: \(29 \times 2 = 58\).
- Subtract 5: \(58 - 5 = 53\).

4. **From 53 to 113**:
- Multiply 53 by 2: \(53 \times 2 = 106\).
- Add 7: \(106 + 7 = 113\).

5. **From 113 to 217**:
- Multiply 113 by 2: \(113 \times 2 = 226\).
- Subtract 9: \(226 - 9 = 217\).

### Step 2: Establish the pattern
The pattern alternates between multiplying by 2 and then either subtracting or adding an odd number:
- -1, +3, -5, +7, -9.

### Step 3: Apply the pattern to the second series
The second series starts with 5:
5, A, B, C, D, E.

1. **Finding A**:
- Multiply 5 by 2: \(5 \times 2 = 10\).
- Subtract 1: \(10 - 1 = 9\).
- So, A = 9.

2. **Finding B**:
- Multiply 9 by 2: \(9 \times 2 = 18\).
- Add 3: \(18 + 3 = 21\).
- So, B = 21.

3. **Finding C**:
- Multiply 21 by 2: \(21 \times 2 = 42\).
- Subtract 5: \(42 - 5 = 37\).
- So, C = 37.

4. **Finding D**:
- Multiply 37 by 2: \(37 \times 2 = 74\).
- Add 7: \(74 + 7 = 81\).
- So, D = 81.

5. **Finding E**:
- Multiply 81 by 2: \(81 \times 2 = 162\).
- Subtract 9: \(162 - 9 = 153\).
- So, E = 153.

### Final Answer
Thus, the value that will come in place of E is **153**.

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