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# If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

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Updated on: 12 Apr 2018, 00:46
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:03) correct 48% (02:07) wrong based on 117 sessions

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[GMAT math practice question]

If $$R_{n+1}-R_n=(\frac{-1}{2})^n$$ for positive integers $$n$$, which of the following is true?

A. $$R_1>R_3 >R_2$$

B. $$R_1>R_2 >R_3$$

C. $$R_3 >R_1 >R_2$$

D. $$R_2>R_3 >R_1$$

E. $$R_3>R_2>R_1$$

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 06 Apr 2018, 00:03. Last edited by Bunuel on 12 Apr 2018, 00:46, edited 2 times in total. Edited the question. Director Joined: 21 May 2013 Posts: 659 Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is [#permalink] ### Show Tags 06 Apr 2018, 01:12 MathRevolution wrote: [GMAT math practice question] If $$R_{n+1}-R_n=(\frac{-1}{2})^n$$ for positive integers $$n$$, which of the following is true? A. $$R_1>R_3 >R_2$$ B. $$R_1>R_2 >R_3$$ C. $$R_3 >R_1 >R_2$$ D. $$R_2>R_3 >R_1$$ E. $$R_3>R_2>R_1$$ I think answer should be A . R2-R1=-1/2 R3-R2=1/4 Adding both equations R3-R1=-1/4 Therefore, R1>R3>R2 Can you please confirm? Bunuel Manager Joined: 24 Mar 2018 Posts: 182 Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is [#permalink] ### Show Tags 06 Apr 2018, 03:13 the option A should be correct Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is [#permalink] ### Show Tags Updated on: 25 Jul 2018, 13:19 => If $$n = 1$$, then R2 – R1 = $$-(\frac{1}{2}) < 0$$, and we have R1 > R2. If $$n = 2$$, then R3 – R2 = $$\frac{1}{4} > 0$$, and we have R3 > R2. Furthermore, R3 – R1 = ( R3 – R2 ) + ( R2 – R1 ) = $$\frac{1}{4} + (\frac{-1}{2})$$ =$$\frac{-1}{4} < 0$$, and we have R3 < R1. Thus R1 > R3 > R2. Therefore, A is the answer. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Originally posted by MathRevolution on 08 Apr 2018, 17:16.
Last edited by MathRevolution on 25 Jul 2018, 13:19, edited 1 time in total.
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Joined: 27 Aug 2016
Posts: 15
Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

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12 Apr 2018, 00:42
MathRevolution wrote:
=>

If $$n = 1$$, then R2 – R1 = $$-(\frac{1}{2}) < 0$$, and we have R1 > R2.
If $$n = 2$$, then R3 – R2 = $$\frac{1}{4} > 0$$, and we have R3 > R2.
Furthermore, R3 – R1 = ( R3 – R2 ) + ( R2 – R1 ) = $$\frac{1}{4} + (\frac{-1}{2})$$ =$$\frac{-1}{4} < 0$$, and we have R3 < R1.
Thus R1 > R3 > R2.

The answer obtained points to Option A and not Option C.

Kindly modify the OA.
Director
Joined: 27 May 2012
Posts: 671
Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

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20 Jul 2018, 07:15
MathRevolution wrote:
=>

If $$n = 1$$, then R2 – R1 = $$-(\frac{1}{2}) < 0$$, and we have R1 > R2.
If $$n = 2$$, then R3 – R2 = $$\frac{1}{4} > 0$$, and we have R3 > R2.
Furthermore, R3 – R1 = ( R3 – R2 ) + ( R2 – R1 ) = $$\frac{1}{4} + (\frac{-1}{2})$$ =$$\frac{-1}{4} < 0$$, and we have R3 < R1.
Thus R1 > R3 > R2.

Dear Moderator ,
This post needs your attention. The answer obtained is choice A and NOT choice C. Kindly correct the small typo in the post by MathRevolution. Thank you.
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Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

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20 Jul 2018, 07:56
R2-R1= - 0.5
R3-R2= -1
So, R3-R1= -1.5
There can be a situation when value of R1=3, R2=2.5 R3=1.5 then these values satisfy the above equations. Then R1>R2>R3.
Ans.B
Is this approach right ???

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Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

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20 Jul 2018, 10:16
BARUAH wrote:
R2-R1= - 0.5
R3-R2= -1
So, R3-R1= -1.5
There can be a situation when value of R1=3, R2=2.5 R3=1.5 then these values satisfy the above equations. Then R1>R2>R3.
Ans.B
Is this approach right ???

Sent from my Lenovo K33a42 using GMAT Club Forum mobile app

How did you get $$R_3 -R_2= -1$$ ?
$$R_3-R_2 = \frac{1}{4}$$ because $$R_3-R_2$$ = $$(\frac{-1}{2})^2$$
Remember the stem $$R _{n+1} -R_n = (\frac{-1}{2})^n$$

So for n= 2 , $$(\frac{-1}{2})^2$$

Hope this helps, please feel free to ask if anything is still unclear.
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Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

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25 Jul 2018, 11:37
(I) R2 - R1 = -1/2 = -0.50
(II) R3 - R2 = +1/4 = +0.25
(III) R3 - R1 = -1/4 = -0.25

We can see that R1 > R3 > R2

If it's not clear, you can change the variables for numbers
R2 = 0.50
R1 = 1.00
R3 = 0.75

(I) R2 - R1 = -1/2 = -0.50
0.5 - 1.0 = -0.50

(II) R3 - R2 = +1/4 = +0.25
0.75 - 0.50 = +0.25

(III) R3 - R1 = -1/4 = -0.25
0.75 - 1.00 = -0.25

1.00 > 0.75 > 0.50
R1 > R3 > R2

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Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is &nbs [#permalink] 25 Jul 2018, 11:37
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