In an arithmetic sequence, there is a ratio that is added for each subsequent number (for example: 2, 4, 6, 8, ...), and in the geometric sequence, the ratio is multiplied instead of being added (for example: 2, 4, 8, 16, ...).
So in the sequence 20, 10, 5, we can see that each subsequent number is half the previous one, that is, the number is multilplied by 0.5.
So in this case we have a geometric sequence, because we have a ratio that is being multilplied for every new number.