Find the missing number in the following series . 27,29,33,? 57

Options

A. (A)30
B. (B)41
C. (C)40
D. (D)35

Answer

To find the missing number in the series 27, 29, 33, ?, 57, we can follow these steps:

### Step 1: Identify the series
The given series is: 27, 29, 33, ?, 57.

### Step 2: Find the differences between consecutive numbers
- The difference between 27 and 29 is:
\[ 29 - 27 = 2 \]
- The difference between 29 and 33 is:
\[ 33 - 29 = 4 \]

### Step 3: Look for a pattern in the differences
The differences we have found are:
- First difference: 2
- Second difference: 4

We can see that the differences are increasing. Let's assume the next difference will follow a pattern.

### Step 4: Predict the next difference
If we observe the pattern, it seems that the differences are doubling:
- 2 (first difference)
- 4 (second difference)
- If we continue this pattern, the next difference should be:
\[ 8 \quad (\text{double of } 4) \]

### Step 5: Calculate the missing number
Now, we add this predicted difference (8) to the last known number in the series (33):
\[ 33 + 8 = 41 \]

### Step 6: Verify the next difference
Next, we need to check if the next number (41) leads us correctly to the final number in the series (57):
- The difference between 41 and 57 should be:
\[ 57 - 41 = 16 \]
This fits our pattern since 16 is double of 8.

### Conclusion
Thus, the missing number in the series is:
\[ \boxed{41} \]