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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]  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]  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!
Re: Each number SN in a sequence can be expressed as a function   [#permalink] 20 Sep 2017, 05:39
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