`{:("3","1.5","1.5","2.25","4.5","11.25"),("4.5","(A)","(B)","(C)","(D)","(E)"):}`
Out of the following, which number will replace (D)?

Options

A. 6.75
B. 11.25
C. 2.25
D. 16.875

Explanation

To solve the problem, we need to identify the pattern in the first series and apply it to the second series to find the value that will replace (D).

### Step-by-step Solution:

1. **Identify the First Series**: The first series is given as 3, 1.5, 2.25, 4.5, 11.25.

2. **Determine the Pattern**:
- From 3 to 1.5: \( 3 \times 0.5 = 1.5 \)
- From 1.5 to 2.25: \( 1.5 \times 1.5 = 2.25 \)
- From 2.25 to 4.5: \( 2.25 \times 2 = 4.5 \)
- From 4.5 to 11.25: \( 4.5 \times 2.5 = 11.25 \)

The multipliers are: 0.5, 1.5, 2, and 2.5. We can see that the multiplier increases by 0.5 each time.

3. **Apply the Pattern to the Second Series**: The second series starts with 4.5 and we need to find the values for A, B, C, and D.

- **Finding A**:
- \( 4.5 \times 0.5 = 2.25 \) (So, A = 2.25)

- **Finding B**:
- \( 2.25 \times 1 = 2.25 \) (So, B = 2.25)

- **Finding C**:
- \( 2.25 \times 1.5 = 3.375 \) (So, C = 3.375)

- **Finding D**:
- \( 3.375 \times 2 = 6.75 \) (So, D = 6.75)

4. **Final Answer**: The number that will replace (D) is **6.75**.