What should come in place of X in the given series? 3 9 21 41 71 X

The correct option is 113.

To find the missing number X in the given series, let us analyze the differences between consecutive terms:

9 - 3 = 6
21 - 9 = 12
41 - 21 = 20
71 - 41 = 30

Now, let us examine the pattern formed by these first-level differences (6, 12, 20, 30):

12 - 6 = 6
20 - 12 = 8
30 - 20 = 10

The second-level differences are increasing by 2 each time (6, 8, 10). Following this pattern, the next second-level difference should be:

10 + 2 = 12

Adding this to the last first-level difference (30), we get the difference to be added to 71:

30 + 12 = 42

Therefore, the value of X is:

X = 71 + 42 = 113