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Each number SN in a sequence can be expressed as a function

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Each number SN in a sequence can be expressed as a function [#permalink] New post 15 Jun 2017, 07:33
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Each number SN in a sequence can be expressed as a function of the preceding number (SN–1) as follows: SN = \(\frac{2}{3}\) SN–1 – 4. Which of the following equations correctly expresses the value of SN in this sequence in terms of SN+2?

A) Sn = \(\frac{9}{4}\) Sn+2 +18

B) Sn = \(\frac{4}{9}\) Sn+2 +15

C) Sn = \(\frac{9}{4}\) Sn+2 + 15

D) Sn = \(\frac{4}{9}\) Sn+2 - 8

E) Sn = \(\frac{2}{3}\) Sn+2 -8
[Reveal] Spoiler: OA

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Re: Each number SN in a sequence can be expressed as a function [#permalink] New post 20 Sep 2017, 05:39
Given the rule for \(S_n\), \(S_{n+2}=\frac{2}{3}S_{n+1}-4\). Then, using the same rule, we know that \(S_{n+1}=\frac{2}{3}S_n-4\) and we can substitute this in the expression for \(S_{n+2}\), which gives us \(S_{n+2}=\frac{2}{3}(\frac{2}{3}S_n-4)-4\). Using easy algebra, we get \(S_n=\frac{9}{4}S_{n+2}+15\). Answer C!
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Re: Each number SN in a sequence can be expressed as a function [#permalink] New post 27 Dec 2017, 03:36
Can I get a further explanation on this problem? I'm not understanding exactly how to solve.

Thank you,
Re: Each number SN in a sequence can be expressed as a function   [#permalink] 27 Dec 2017, 03:36
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Each number SN in a sequence can be expressed as a function

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