What should come in place of the question mark (?) in the following number series ?
`25" "26" "40" "81" "?" "611.5`

Options

A. 302.5
B. 103.5
C. 203.5
D. 303.5

Answer

To find the missing number in the series: 25, 26, 40, 81, ?, 611.5, we will analyze the pattern in the sequence step by step.

### Step 1: Identify the pattern between the numbers
- The first number is 25.
- The second number is 26, which can be derived from 25 by multiplying it by 1 and adding 1:
\[ 25 \times 1 + 1 = 26 \]

### Step 2: Find the relationship from 26 to 40
- The next number is 40. To get from 26 to 40, we can use the following calculation:
\[ 26 \times \frac{3}{2} + 1 = 39 + 1 = 40 \]

### Step 3: Find the relationship from 40 to 81
- Now, we need to find how to get from 40 to 81:
\[ 40 \times 2 + 1 = 80 + 1 = 81 \]

### Step 4: Find the relationship from 81 to the missing number
- Next, we need to find the missing number (let's call it x) after 81:
\[ 81 \times \frac{5}{2} + 1 = 202.5 + 1 = 203.5 \]

### Step 5: Find the relationship from the missing number to 611.5
- Finally, we check the relationship from the missing number (203.5) to 611.5:
\[ 203.5 \times 3 + 1 = 610.5 + 1 = 611.5 \]

### Conclusion
Thus, the missing number in the series is:
\[ \boxed{203.5} \]