Question

the sequence 20, 16, 12, ... is an example of what type of sequence?
a. finite
b. cyclical
c. geometric
d. arithmetic

Explanation:

To determine the type of sequence \(20, 16, 12, \dots\):

• Finite: A finite sequence has a limited number of terms; this sequence has "\(\dots\)", so it's infinite, eliminating option a.
• Cyclical: A cyclical sequence repeats values in a cycle, which is not the case here, eliminating option b.
• Geometric: A geometric sequence has a common ratio (multiplier) between terms. Here, \(\frac{16}{20} = 0.8\) and \(\frac{12}{16} = 0.75\) (not constant), so it is not geometric, eliminating option c.
• Arithmetic: An arithmetic sequence has a common difference (subtraction/addition) between terms. Here, \(16 - 20 = -4\) and \(12 - 16 = -4\) (constant difference of \(-4\)), so it is arithmetic.

Answer:

d. Arithmetic