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.
`{:("9","10","16","57","212","1085"),("2","A","B","C","D","E"):}`
What will come in place of C?

Options

A. 37
B. 15
C. 18
D. 25

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 C.

### Step-by-Step Solution:

1. **Identify the Pattern in the First Series:**
The first series is: 9, 10, 16, 57, 212, 1085.
- From 9 to 10: \(9 \times 1 + 1 = 10\)
- From 10 to 16: \(10 \times 2 - 4 = 16\)
- From 16 to 57: \(16 \times 3 + 9 = 57\)
- From 57 to 212: \(57 \times 4 - 16 = 212\)
- From 212 to 1085: \(212 \times 5 + 25 = 1085\)

The pattern involves multiplying by an increasing integer (1, 2, 3, 4, 5) and then adding or subtracting the square of that integer alternately.

2. **Apply the Pattern to the Second Series:**
The second series starts with 2 and is represented as: 2, A, B, C, D, E.
- **Finding A:**
- \(2 \times 1 + 1^2 = 2 \times 1 + 1 = 2 + 1 = 3\)
- So, A = 3.

- **Finding B:**
- \(A \times 2 - 2^2 = 3 \times 2 - 4 = 6 - 4 = 2\)
- So, B = 2.

- **Finding C:**
- \(B \times 3 + 3^2 = 2 \times 3 + 9 = 6 + 9 = 15\)
- So, C = 15.

### Final Answer:
C = 15.