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.
`{:("616","496","397","317","254",),("838","A","B","C","D","E"):}`
What will come in place of E?

Options

A. 428
B. 619
C. 476
D. 529

Explanation

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

### Step-by-Step Solution:

1. **Identify the First Series:**
The first series is:
- 616, 496, 397, 317, 254

2. **Calculate the Differences:**
We will find the differences between consecutive terms:
- 616 - 496 = 120
- 496 - 397 = 99
- 397 - 317 = 80
- 317 - 254 = 63

So, the differences are:
- 120, 99, 80, 63

3. **Recognize the Pattern in Differences:**
We can see that these differences can be expressed as:
- 120 = 11² - 1
- 99 = 10² - 1
- 80 = 9² - 1
- 63 = 8² - 1

This suggests that the differences are decreasing squares minus one.

4. **Continue the Pattern:**
Following this pattern, the next difference should be:
- 7² - 1 = 49 - 1 = 48

5. **Apply the Pattern to the Second Series:**
The second series starts with 838 and has elements represented as:
- 838, A, B, C, D, E

6. **Calculate A:**
To find A, we subtract the first difference (120) from 838:
- A = 838 - 120 = 718

7. **Calculate B:**
To find B, we subtract the second difference (99) from A:
- B = 718 - 99 = 619

8. **Calculate C:**
To find C, we subtract the third difference (80) from B:
- C = 619 - 80 = 539

9. **Calculate D:**
To find D, we subtract the fourth difference (63) from C:
- D = 539 - 63 = 476

10. **Calculate E:**
Finally, to find E, we subtract the fifth difference (48) from D:
- E = 476 - 48 = 428

### Final Answer:
The value that comes in place of E is **428**.