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Use the following chart to develop an explicit formula for the geometric sequence. Choose the correct formula. Input (n) Output f(n) 1 3 2 3 4 5 6 -6 12 -24 48 -96

Use the following chart to develop an explicit formula for the geometric sequence. Choose the correct formula. Input (n) Output f(n) 1 3 2 3 4 5 6 -6 12 -24 48 -96

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Developing an Explicit Formula for a Geometric Sequence Use the following chart to develop an explicit formula for the geometric sequence. Choose the correct formula. | Input (n) | Output (f(n)) | |-----------|---------------| | 1 | 3 | | 2 | -6 | | 3 | 12 | | 4 | -24 | | 5 | 48 | | 6 | -96 | #### Options: - **a.** \( f(n) = 3 * 3^{n-1} \) - **b.** \( f(n) = 3 * 2^{n-1} \) - **c.** \( f(n) = 3 * (-2)^{n-1} \) - **d.** \( f(n) = 3 * (-3)^n \) Consider each option and determine which one fits the values provided in the chart. The goal is to identify the correct formula that represents the given sequence.
Transcribed Image Text:### Developing an Explicit Formula for a Geometric Sequence Use the following chart to develop an explicit formula for the geometric sequence. Choose the correct formula. | Input (n) | Output (f(n)) | |-----------|---------------| | 1 | 3 | | 2 | -6 | | 3 | 12 | | 4 | -24 | | 5 | 48 | | 6 | -96 | #### Options: - **a.** \( f(n) = 3 * 3^{n-1} \) - **b.** \( f(n) = 3 * 2^{n-1} \) - **c.** \( f(n) = 3 * (-2)^{n-1} \) - **d.** \( f(n) = 3 * (-3)^n \) Consider each option and determine which one fits the values provided in the chart. The goal is to identify the correct formula that represents the given sequence.
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