What should come in place of the question mark (?) in the following number series ?
`110" "300" "?" "1962.5" "4931.25`

Options

A. 800
B. 575
C. 775
D. 885

Answer

To solve the number series problem: `110, 300, ?, 1962.5, 4931.25`, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the first two terms**: The first term is 110 and the second term is 300.

2. **Calculate the difference**:
- The difference between the first and second terms is:
\[ 300 - 110 = 190 \]

3. **Look for a multiplication factor**:
- To see if there's a multiplication factor, we can check if multiplying the first term by a certain number can give us the second term.
- If we multiply 110 by 2.5, we get:
\[ 110 \times 2.5 = 275 \]
- This is not equal to 300, but we can add a number to it. Let's check:
\[ 275 + 25 = 300 \]

4. **Apply the same logic to find the next term**:
- Now, we take the second term (300) and apply the same multiplication factor (2.5):
\[ 300 \times 2.5 = 750 \]
- Then, we add 25 to this result:
\[ 750 + 25 = 775 \]
- So, the third term (the one we need to find) is 775.

5. **Verify the next terms**:
- Now, let's check if this pattern holds for the next terms. We take the third term (775) and multiply by 2.5:
\[ 775 \times 2.5 = 1937.5 \]
- Adding 25 gives:
\[ 1937.5 + 25 = 1962.5 \]
- This matches the fourth term.

6. **Check the last term**:
- Now, for the last term, we take 1962.5 and multiply by 2.5:
\[ 1962.5 \times 2.5 = 4906.25 \]
- Adding 25 gives:
\[ 4906.25 + 25 = 4931.25 \]
- This matches the last term.

### Conclusion:
The missing term in the series is **775**.