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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
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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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New post Updated on: 12 Apr 2018, 01:46
00:00
A
B
C
D
E

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  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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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.
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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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New post 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
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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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New post 06 Apr 2018, 04:13
the option A should be correct
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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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New post 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
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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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New post 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.

Therefore, C is the answer.
Answer: C


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

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