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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
Posts: 5245
GMAT 1: 800 Q59 V59
GPA: 3.82
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, 01:46
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Difficulty:

95% (hard)

Question Stats:

42% (01:14) correct 58% (01:44) wrong based on 39 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. $$R_3>R_2>R_1$$
[Reveal] Spoiler: OA

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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 $79 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, 01:03. Last edited by Bunuel on 12 Apr 2018, 01:46, edited 2 times in total. Edited the question. Director Joined: 21 May 2013 Posts: 621 Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is [#permalink] ### Show Tags 06 Apr 2018, 02:12 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 Intern Joined: 24 Mar 2018 Posts: 24 Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is [#permalink] ### Show Tags 06 Apr 2018, 04:13 the option A should be correct Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5245 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is [#permalink] ### Show Tags 08 Apr 2018, 18:16 => 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, C is the answer. Answer: C _________________ 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$79 for 3 month Online Course"
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Joined: 27 Aug 2016
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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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12 Apr 2018, 01:42
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.
Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is   [#permalink] 12 Apr 2018, 01:42
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