Write a recursive sequence that represents the sequence defined by the following explicit formula: an=-405(-1/3)^n+1

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LuccianoU361443 LuccianoU361443

03-11-2022
Mathematics

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Write a recursive sequence that represents the sequence defined by the following explicit formula: an=-405(-1/3)^n+1

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CateleyaX223880 CateleyaX223880 · Answer 1 · 2022-11-03T11:08:01+01:00

[tex]\begin{gathered} \text{ an = -405(-}\frac{1}{3})^{n\text{ + 1}} \\ \text{ a}_1\text{ = -405(-}\frac{1}{3})^{1\text{ + 1}}\text{ = -405(-}\frac{1}{3})^2\text{ = -405(}\frac{1}{9})\text{ = -45} \end{gathered}[/tex]

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[tex]\begin{gathered} \text{ an = -405(-}\frac{1}{3})^{n\text{ + 1 - 1}} \\ \text{ an = -405(-}\frac{1}{3})^n \end{gathered}[/tex]