GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jul 2018, 04:03

### 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

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

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5866
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: 12 Apr 2018, 01:46
00:00

Difficulty:

85% (hard)

Question Stats:

44% (01:09) correct 56% (01:44) wrong based on 77 sessions

### HideShow timer Statistics

[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. $$R_3>R_2>R_1$$

_________________

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 $99 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: 651 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 Manager Joined: 24 Mar 2018 Posts: 64 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: 5866 GMAT 1: 760 Q51 V42 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$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 27 Aug 2016
Posts: 13
Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

### Show Tags

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.
Director
Joined: 27 May 2012
Posts: 513
Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

### Show Tags

20 Jul 2018, 08:15
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.
_________________

- Stne

Intern
Joined: 25 Nov 2017
Posts: 20
Location: India
Schools: IIMA , IIMB, IIMC
GMAT 1: 590 Q47 V25
GMAT 2: 700 Q50 V34
GPA: 3.56
Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

### Show Tags

20 Jul 2018, 08:56
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 ???

Sent from my Lenovo K33a42 using GMAT Club Forum mobile app
Director
Joined: 27 May 2012
Posts: 513
Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is  [#permalink]

### Show Tags

20 Jul 2018, 11:16
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.
_________________

- Stne

Re: If Rn+1-Rn=(-1/2)n for positive integers n, which of the following is &nbs [#permalink] 20 Jul 2018, 11:16
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.