What value will come in place of question mark (?) in the questions given below?
`8, 12, 30, 105, ?, 2598.75`

Options

A. `471.5`
B. `472.5`
C. `473.5`
D. `470.5`

Answer

To find the missing value in the sequence `8, 12, 30, 105, ?, 2598.75`, we will analyze the pattern in the numbers.

### Step-by-Step Solution:

1. **Identify the pattern**:
- The first number is **8**.
- The second number is **12**.
- The third number is **30**.
- The fourth number is **105**.

2. **Calculate the relationship between the numbers**:
- From **8 to 12**:
\[ 12 = 8 \times 1.5 \]
- From **12 to 30**:
\[ 30 = 12 \times 2.5 \]
- From **30 to 105**:
\[ 105 = 30 \times 3.5 \]

3. **Identify the multiplier pattern**:
- The multipliers are: **1.5, 2.5, 3.5**.
- We can see that the multipliers increase by **1** each time.

4. **Find the next multiplier**:
- The next multiplier after **3.5** would be **4.5**.

5. **Calculate the fifth number**:
- We will multiply the fourth number **105** by the next multiplier **4.5**:
\[ ? = 105 \times 4.5 \]
- Performing the multiplication:
\[ 105 \times 4.5 = 472.5 \]

6. **Confirm the sixth number**:
- The sixth number should be **2598.75**.
- We need to check if multiplying the fifth number **472.5** by the next multiplier **5.5** gives us **2598.75**:
\[ 2598.75 = 472.5 \times 5.5 \]
- Performing the multiplication:
\[ 472.5 \times 5.5 = 2598.75 \]
- This confirms our calculations.

### Final Answer:
The value that comes in place of the question mark (?) is **472.5**.