It is currently 17 Jun 2019, 22:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 6885
Followers: 114

Kudos [?]: 1338 [1] , given: 6306

Each number SN in a sequence can be expressed as a function [#permalink]  15 Jun 2017, 07:33
1
This post received
KUDOS
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
Followers: 1

Kudos [?]: 356 [0], given: 66

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!
Intern
Joined: 27 Dec 2017
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Each number SN in a sequence can be expressed as a function [#permalink]  27 Dec 2017, 03:36
Can I get a further explanation on this problem? I'm not understanding exactly how to solve.

Thank you,
Intern
Joined: 04 Dec 2018
Posts: 30
Followers: 0

Kudos [?]: 8 [0], given: 4

Re: Each number SN in a sequence can be expressed as a function [#permalink]  11 Dec 2018, 18:15
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
C is the answer
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 111 [0], given: 4

Re: Each number SN in a sequence can be expressed as a function [#permalink]  11 Dec 2018, 23:27
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
Display posts from previous: Sort by

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

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.