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","40","176","537","1078","1079"),("1","A","B","C","D","E"):}`
What will come in place of E?

Options

A. 839
B. 738
C. 829
D. 938

Explanation

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

### Step 1: Analyze the First Series
The first series is:
3, 40, 176, 537, 1078, 1079.

1. **Identify the pattern:**
- From 3 to 40:
- Multiply 3 by 5 and add \(5^2\) (which is 25).
- \(3 \times 5 + 25 = 15 + 25 = 40\).
- From 40 to 176:
- Multiply 40 by 4 and add \(4^2\) (which is 16).
- \(40 \times 4 + 16 = 160 + 16 = 176\).
- From 176 to 537:
- Multiply 176 by 3 and add \(3^2\) (which is 9).
- \(176 \times 3 + 9 = 528 + 9 = 537\).
- From 537 to 1078:
- Multiply 537 by 2 and add \(2^2\) (which is 4).
- \(537 \times 2 + 4 = 1074 + 4 = 1078\).
- From 1078 to 1079:
- Multiply 1078 by 1 and add \(1^2\) (which is 1).
- \(1078 \times 1 + 1 = 1078 + 1 = 1079\).

### Step 2: Establish the Pattern
The pattern observed is:
- For the nth term, multiply the previous term by \(6 - n\) and add \((6 - n)^2\).

### Step 3: Apply the Pattern to the Second Series
The second series is:
1, A, B, C, D, E.

1. **Calculate A:**
- Start with 1.
- \(1 \times 5 + 5^2 = 1 \times 5 + 25 = 5 + 25 = 30\).
- So, A = 30.

2. **Calculate B:**
- \(30 \times 4 + 4^2 = 30 \times 4 + 16 = 120 + 16 = 136\).
- So, B = 136.

3. **Calculate C:**
- \(136 \times 3 + 3^2 = 136 \times 3 + 9 = 408 + 9 = 417\).
- So, C = 417.

4. **Calculate D:**
- \(417 \times 2 + 2^2 = 417 \times 2 + 4 = 834 + 4 = 838\).
- So, D = 838.

5. **Calculate E:**
- \(838 \times 1 + 1^2 = 838 \times 1 + 1 = 838 + 1 = 839\).
- So, E = 839.

### Final Answer
The value that comes in place of E is **839**.