In a geometric sequence you get the (n+1)'th term by multiplying the n'th term by the common ratio r.
To test if 3,12,36 ... are the terms of a geometric sequence we calculate the common ratio for 3 and 12 ,and 12 and 36. Thus:
r = 12/3 = 4 and r = 36/12 = 3
Since 4 is not equal to 3 there is not a constant common ratio and hence this is not a geometric sequence.
