Question
Which of the following best describes this sequence? \( \{32,20,8,-4, \ldots\} \) Arithmetic Neither Both Geometric
Ask by Li Burns. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sequence is arithmetic.
Solution
To determine which type the sequence is, check the differences between consecutive terms:
20 − 32 = -12
8 − 20 = -12
-4 − 8 = -12
Since the difference is constant at -12, the sequence is arithmetic.
The correct answer is: Arithmetic.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
This sequence is arithmetic! In fact, if you take a closer look, each term is derived by subtracting 12 from the previous term: \(32 - 12 = 20\), \(20 - 12 = 8\), and so on. So, it's a consistent pattern of taking away 12 at every step. On the other hand, for it to be geometric, we'd need to multiply by a constant factor to get from one term to the next, which isn't happening here. So, that's why it fits snugly into the arithmetic category and leaves geometric in the dust!
