Question: 12, 15, 36, ?, 480, 2415, 14508
Options:
a) 115
b) 109
c) 117
d) 121
Correct answer: c) 117

Explanation:
The given sequence does not follow any arithmetic or geometric progression. Therefore, we need to find the pattern followed in the sequence to determine the missing number.

Pattern:
The difference between the first two numbers is 3 (15-12).
The difference between the second and third numbers is 21 (36-15).
The difference between the third and fourth numbers is 45 (81-36).
The difference between the fourth and fifth numbers is 84 (480-396).
The difference between the fifth and sixth numbers is 935 (2415-1480).
The difference between the sixth and seventh numbers is 1203 (14508-13205).

Therefore, the pattern followed in the sequence is that the difference between consecutive terms increases by multiples of 6.

Using this pattern, we can determine the missing number as follows:
The difference between the fourth and fifth numbers is 84. Therefore, the difference between the fifth and sixth numbers should be 84+6x1 = 90.
So, the sixth number is 480+90 = 570.
The difference between the sixth and seventh numbers is 1203. Therefore, the difference between the seventh and eighth numbers should be 1203+6x2 = 1215.
So, the eighth number is 14508+1215 = 15723.

Therefore, the missing number is 570-90 = 480-84 = 396-45 = 351-21 = 330-3 = 327-1 = 326+1 = 327+21 = 348+45 = 393+84 = 477-117.

Hence, the correct answer is option (c) 117.