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","4","16","75","364","1945"),("1","A","B","C","D","E"):}`
What will come in place of C?

Options

A. 72
B. 63
C. 66
D. 69

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: 3, 4, 16, 75, 364, 1945.

- From 3 to 4:
\[ 3 \times 1 + 1^3 = 3 + 1 = 4 \]
- From 4 to 16:
\[ 4 \times 2 + 2^3 = 8 + 8 = 16 \]
- From 16 to 75:
\[ 16 \times 3 + 3^3 = 48 + 27 = 75 \]
- From 75 to 364:
\[ 75 \times 4 + 4^3 = 300 + 64 = 364 \]
- From 364 to 1945:
\[ 364 \times 5 + 5^3 = 1820 + 125 = 1945 \]

The pattern observed is that each term is obtained by multiplying the previous term by a consecutive integer and adding the cube of that integer.

2. **Apply the Pattern to the Second Series:**
The second series is: 1, A, B, C, D, E.

- **Finding A:**
\[ 1 \times 1 + 1^3 = 1 + 1 = 2 \quad \text{(So, A = 2)} \]

- **Finding B:**
\[ 2 \times 2 + 2^3 = 4 + 8 = 12 \quad \text{(So, B = 12)} \]

- **Finding C:**
\[ 12 \times 3 + 3^3 = 36 + 27 = 63 \quad \text{(So, C = 63)} \]

3. **Conclusion:**
The value that comes in place of C is **63**.