`{:(5,9,25,91,414,2282.5),(3,(a),(b),(c),(d),(e)):}`
What will come in place of (c) ?

Options

A. 63.25
B. 63.75
C. 64.25
D. 64.75

Explanation

To solve the problem and find the value that comes in place of (c) in the series `{:(5,9,25,91,414,2282.5),(3,(a),(b),(c),(d),(e)):}`, we will follow the pattern established in the series step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The series seems to follow a pattern where each term is derived from the previous term by multiplying it by a certain factor and then adding a constant.

2. **Calculate the First Few Terms**:
- Starting with **5**:
\[ 5 \times 1.5 + 1.5 = 7.5 \quad \text{(but we actually need to add it to get to 9)} \]
So, \( 5 \times 1.5 + 1.5 = 9 \) (correct).

- Next, for **9**:
\[ 9 \times 2.5 + 2.5 = 22.5 \quad \text{(but we need to add it to get to 25)} \]
So, \( 9 \times 2.5 + 2.5 = 25 \) (correct).

- Next, for **25**:
\[ 25 \times 3.5 + 3.5 = 91 \quad \text{(correct)}. \]

- Next, for **91**:
\[ 91 \times 4.5 + 4.5 = 409.5 \quad \text{(but we need to add it to get to 414)} \]
So, \( 91 \times 4.5 + 4.5 = 414 \) (correct).

3. **Continue the Pattern**:
- Now, we need to find the next term after **414**:
\[ 414 \times 5.5 + 5.5 = 2282.5 \quad \text{(correct)}. \]

4. **Now, Calculate for the Second Series**:
- Start with **3**:
\[ 3 \times 1.5 + 1.5 = 4.5. \]

- Next, we add 1.5:
\[ 4.5 + 1.5 = 6. \]

- For **(a)**, we have **6**:
\[ 6 \times 2.5 + 2.5 = 15. \]

- Next, we add 2.5:
\[ 15 + 2.5 = 17.5 \quad \text{(this is (b))}. \]

5. **Calculate (c)**:
- Now for (c):
\[ 17.5 \times 3.5 + 3.5 = 61.25. \]

- Next, we add 3.5:
\[ 61.25 + 3.5 = 64.75 \quad \text{(this is (c))}. \]

### Final Answer:
The value that comes in place of (c) is **64.75**.