Given the expression;
300, 100, 100/3, 100/9...
This sequence is geometric sequence because they have a common ratio not common difference.
Given the set of Geometric sequence, T1, T2, T3, T4... the common ratio is calculated as thus;
r = T2/T1 = T3/T2 = T4/T3
From the given sequence;
300, 100, 100/3, 100/9...
r = 100/300 = (100/3)/100 = (100/9)/(100/3)
r = 1/3
Hence the common ratio is 1/3 and the sequence is a Geometric sequence