Question
Which of the following best describes this sequence? \( \{2,-4,8,-16,32, \ldots\} \) Geometric Neither Both Arithmetic
Ask by Riley Ayala. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sequence is geometric.
Solution
To determine the type of sequence, we first check for a constant ratio between consecutive terms. The given sequence is:
2, -4, 8, -16, 32, ...
We find the ratio by dividing each term by the previous term:
(-4) / 2 = -2
8 / (-4) = -2
(-16) / 8 = -2
Since the ratio is consistently -2, the sequence is a geometric sequence with common ratio -2.
Thus, the best description for this sequence is: Geometric.
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Simplify this solution Bonus Knowledge
This sequence is geometric! Each term is multiplied by -2 to get the next term: \( 2 \times -2 = -4 \), \( -4 \times -2 = 8 \), and so on. The constant ratio of -2 between consecutive terms is the defining characteristic of a geometric sequence. Fun fact: Geometric sequences can model various real-world scenarios such as population growth, financial investments, and even the spread of diseases! They are super handy in fields ranging from economics to biology.
