To determine whether the sequence is arithmetic, geometric, or neither, we need to check the following:
Arithmetic Sequence: An arithmetic sequence has a constant difference between consecutive terms. To check if the given sequence is arithmetic, calculate the differences between consecutive terms:
7 - 12 = -5
2 - 7 = -5
-3 - 2 = -5
Since the difference is consistently -5, the sequence is arithmetic.
Geometric Sequence: A geometric sequence has a constant ratio between consecutive terms. To check if it’s geometric, calculate the ratios: