Sequences
An arithmetic sequence is identified because each term can be found as the sum of the previous term and a constant number called the common difference.
In geometric sequences, each term is found as the previous term times a constant number called the common ratio.
We are given the three first terms of a sequence:
12, 10, 8, ...
If it's a geometric sequence, then the ratio of 10/12 should be equal to the ratio of 8/10. Checking out:
10/12 = 0.83
8/10 = 0.8
Thus, this is NOT a geometric sequence.
Now let's try the differences 10 - 12 and 8 - 10:
10 - 12 = -2
8 - 10 = -2
Since the difference is constant, we have an arithmetic sequence of a common difference of -2.