Finding the Missing Number in the Series

Given series: 3, 9, 24, 57, ?, 267, 552

To find the missing number in the series, we need to identify the pattern followed in the given series. Let's analyze the series step by step:

Step 1: The difference between the first two terms is (9-3) = 6.
Step 2: The difference between the second and third terms is (24-9) = 15.
Step 3: The difference between the third and fourth terms is (57-24) = 33.
Step 4: The difference between the fourth and fifth terms is (?-57).
Step 5: The difference between the fifth and sixth terms is (267-?) = (552-267) = 285.
Step 6: The difference between the sixth and seventh terms is (552-267) = 285.

From the above analysis, we can observe that the differences between the consecutive terms of the series are increasing by a constant difference. Therefore, the missing number in the series can be calculated as follows:

The difference between the fourth and fifth terms is (57-24) = 33.
So, the difference between the fifth and sixth terms should be (33+15) = 48.
Therefore, the missing number in the series is (57+48) = 105.

Hence, the correct answer is option 'B' (126).