Question

classify the following sequence:
12, 8, 4, 0, ...
geometric
neither
arithmetic

Explanation:

Step1: Check for arithmetic sequence

To check if a sequence is arithmetic, we find the difference between consecutive terms.
First difference: \(8 - 12=- 4\)
Second difference: \(4 - 8=-4\)
Third difference: \(0 - 4=-4\)
Since the common difference \(d = - 4\) is constant, we check for geometric sequence.

Step2: Check for geometric sequence

To check if a sequence is geometric, we find the ratio between consecutive terms.
First ratio: \(\frac{8}{12}=\frac{2}{3}\)
Second ratio: \(\frac{4}{8}=\frac{1}{2}\)
Third ratio: \(\frac{0}{4} = 0\)
Since the ratios are not constant, the sequence is not geometric.

Answer:

arithmetic (because the sequence has a constant common difference of -4, so it is an arithmetic sequence)