Find the missing number in the series: 40, 54, 82, ?, 180, 250.

To find the missing number in the series, let's try to identify a pattern or rule that governs the sequence:

40
54
82
? (missing)
180
250
One possible pattern in this sequence is that each number is increasing by a certain amount. Let's calculate the differences between consecutive numbers:

54 - 40 = 14
82 - 54 = 28
180 - 82 = 98
250 - 180 = 70
Now, let's analyze the differences:

The difference between the 1st and 2nd terms is 14.
The difference between the 2nd and 3rd terms is 28, which is twice the difference between the 1st and 2nd terms.
If this pattern continues, the difference between the missing number (4th term) and the 3rd term should be twice the difference between the 2nd and 3rd terms, which is 28 * 2 = 56.

So, to find the missing number:

82 (3rd term) + 56 = 138

Therefore, the missing number in the sequence is 138:

40
54
82
138
180
250