What will come in place of question mark(?) in the given number aeries?
9 5.5 6.5 14 ? 457

Options

A. 53
B. 57
C. 81
D. 49

Answer

To solve the problem of finding the missing number in the series: 9, 5.5, 6.5, 14, ?, 457, we can analyze the pattern of the series step by step.

### Step 1: Analyze the first two numbers
- The first number is 9.
- The second number is 5.5.
- To find how we got from 9 to 5.5, we can observe:
- \( 9 \times 0.5 = 4.5 \)
- Then, \( 4.5 + 1 = 5.5 \)

### Step 2: Analyze the second and third numbers
- The second number is 5.5 and the third number is 6.5.
- We can see:
- \( 5.5 \times 1 = 5.5 \)
- Then, \( 5.5 + 1 = 6.5 \)

### Step 3: Analyze the third and fourth numbers
- The third number is 6.5 and the fourth number is 14.
- Here, we can see:
- \( 6.5 \times 2 = 13 \)
- Then, \( 13 + 1 = 14 \)

### Step 4: Determine the pattern
- From the above steps, we can see a pattern forming:
- First, we multiplied by 0.5 and added 1.
- Second, we multiplied by 1 and added 1.
- Third, we multiplied by 2 and added 1.

- It seems that the multiplier is increasing by doubling each time (0.5, 1, 2). The next multiplier should be 4.

### Step 5: Calculate the missing number
- Now, we need to find the number that comes after 14 using the multiplier of 4:
- \( 14 \times 4 = 56 \)
- Then, \( 56 + 1 = 57 \)

### Step 6: Verify the next number in the series
- The next number after the missing number is 457.
- We can check:
- \( 57 \times 4 = 228 \)
- Then, \( 228 + 1 = 229 \) (which is incorrect for our next number)

- Instead, we should check:
- \( 57 \times 4 = 228 \)
- Then, \( 228 + 1 = 229 \) (this is not leading to 457)

- However, we can check if we multiply 57 by 4:
- \( 57 \times 4 = 228 \)
- Then, \( 228 + 1 = 229 \) (which is incorrect for our next number)

- The correct multiplication should be:
- \( 57 \times 8 = 456 \)
- Then, \( 456 + 1 = 457 \)

### Conclusion
Thus, the missing number in the series is **57**.