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TAGS: Founder  Joined: 18 Apr 2015
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Each number SN in a sequence can be expressed as a function [#permalink]
1
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Expert's post 00:00

Question Stats: 55% (02:15) correct 45% (02:17) wrong based on 40 sessions

Each number $$S_N$$ in a sequence can be expressed as a function of the preceding number ($$S_{N–1}$$) as follows: $$S_N$$= $$\frac{2}{3}$$ $$S_{N–1}$$ $$- 4$$. Which of the following equations correctly expresses the value of SN in this sequence in terms of $$S_{N+2}$$ ?

A) $$S_N$$ = $$\frac{9}{4}$$ $$S_{N+2}$$ $$+18$$

B) $$S_N$$ = $$\frac{4}{9}$$$$S_{N+2}$$ $$+15$$

C) $$S_N$$ = $$\frac{9}{4}$$ $$S_{N+2}$$ $$+ 15$$

D) $$S_N$$ = $$\frac{4}{9}$$ $$S_{N+2}$$ $$- 8$$

E) $$S_N$$ = $$\frac{2}{3}$$ $$S_{N+2}$$ $$-8$$
[Reveal] Spoiler: OA

_________________

Last edited by Carcass on 27 Dec 2018, 03:20, edited 3 times in total.
Edited by Carcass
Director Joined: 03 Sep 2017
Posts: 520
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Re: Each number SN in a sequence can be expressed as a function [#permalink]
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!
Intern Joined: 27 Dec 2017
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Re: Each number SN in a sequence can be expressed as a function [#permalink]
Can I get a further explanation on this problem? I'm not understanding exactly how to solve.

Thank you,
Intern Joined: 04 Dec 2018
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Kudos [?]: 8 , given: 4

Re: Each number SN in a sequence can be expressed as a function [#permalink]
Basically the later number = consecutive earlier number in the sequence times 2/3 then subtracts by 4
Sn
Sn+1 = 2/3 Sn-4
Sn+2=2/3Sn+1−4 = 2/3(2/3Sn -4)-4 = 4/9Sn - 20/3
===> Sn = (Sn+2 + 20/3)*9/4
Sn = 9/4Sn+2 + 15
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Joined: 01 Nov 2017
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Re: Each number SN in a sequence can be expressed as a function [#permalink]
Expert's post
Carcass wrote:

Each number $$S_N$$ in a sequence can be expressed as a function of the preceding number ($$S_{N–1}$$) as follows: $$S_N$$= $$\frac{2}{3}$$ $$S_{N–1}$$ – 4. Which of the following equations correctly expresses the value of SN in this sequence in terms of SN+2?

A) $$S_N$$ = $$\frac{9}{4}$$ $$S_{N+2}$$ +18

B) $$S_N$$ = $$\frac{4}{9}$$$$S_{N+2}$$ +15

C) $$S_N$$ = $$\frac{9}{4}$$ $$S_{N+2}$$ + 15

D) $$S_N$$ = $$\frac{4}{9}$$ $$S_{N+2}$$ - 8

E) $$S_N$$ = $$\frac{2}{3}$$ $$S_{N+2}$$ -8

let u swrite the $$S_N$$= $$\frac{2}{3}$$ $$S_{N–1}$$ – 4 in terms of N+2....
$$S_{N+2}$$= $$\frac{2}{3}$$ $$S_{N+1}$$ – 4, but $$S_{N+1}$$= $$\frac{2}{3}$$ $$S_{N}$$ – 4, so substitute this value in the previous equation..

$$S_{N+2}$$= $$\frac{2}{3}$$ ($$\frac{2}{3}$$ $$S_{N}$$ – 4) – 4 =>$$S_{N+2}$$= $$\frac{2*2}{3*3}$$ $$S_{N}-\frac{2*4}{3}$$ – 4..
=> $$S_{N+2}$$= $$\frac{4}{9}$$ $$S_{N+1}-\frac{8}{3}$$ – 4,
Multiply the equation by 9..
$$9S_{N+2}$$= 4 $$S_{N}$$-8*3 –9* 4 => 4 $$S_{N}=9S_{N+2}$$+60
Divide the entire equation by 4 to get value of $$S_N$$
$$S_{N}=\frac{9}{4}S_{N+2}$$+15

C
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: Each number SN in a sequence can be expressed as a function   [#permalink] 11 Dec 2018, 23:27
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