you have the following sequence:
147, 127, 107, 87, 67, ...
In order to determine if the previous sequence is a geometric sequence or an arimethic one, you take into account the following definitions:
In an arithmetic sequence, you have that each term is the result of the summation of the arithmetic sequence.
In a geometic sequence, the ratio between consecutive term in the sequence is constant.
You can prove if the given sequence is a geometric sequence by dividing consecutive shifts, in order to determine if the ratio are the same:
147/127 = 1.157
127/107 = 1.186
107/87 = 1.229
as you can notice the ratio between consecutive terms are not the same. Then the given sequence is not a geometrical sequence.
However, by the form of the sequence you can notice, that each term is related to the previous one by a simple arithmetic operation, for example
127 = 147 - 20
107 = 127 - 20
87 = 107 - 20
67 = 87 - 20
It's clear that each term is the result of an arithmetic operation that involves the previos term.
Hence, the given sequence is an arithmetic sequence.
The pattern will be:
147,127,107,87,67,47,27,...
147, 147-20, 127-20, 107-20, 87-20, 67-20,...
or, in genereal:
147, 127, 107, ... , (147-20n) n from 0 to infinity