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# A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
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A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?  [#permalink]

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03 Jul 2016, 04:53
00:00

Difficulty:

5% (low)

Question Stats:

89% (02:06) correct 11% (02:35) wrong based on 83 sessions

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A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?

A. 2
B. 3/2
C. 5/3
D. 8/5
E. 13/8

*An answer will be posted in 2 days.

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Joined: 06 Jul 2015
Posts: 20
Re: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?  [#permalink]

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03 Jul 2016, 09:06
This simplifies to A(n+1) * A(n) = A(n) + 1.
A(2) * A(1) = A(1) + 1 => A(2) = 2
A(3) * A(2) = A(2) + 1 => A(3) = 3/2
A(4) * A(3) = A(3) + 1 => A(4) = 5 /3
A(5) * A(4) = A(4) + 1 => A(5) = 8 / 5
Manager
Joined: 22 Jun 2016
Posts: 245
Re: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?  [#permalink]

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03 Jul 2016, 09:09
1
Solve to get:
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5

------------------------------

P.S. Don't forget to give kudos
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P.S. Don't forget to give Kudos

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
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GPA: 3.82
Re: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?  [#permalink]

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04 Jul 2016, 22:31
If we substitute directly, the answer comes out to be D.
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Re: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?  [#permalink]

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21 Oct 2017, 05:34
what does it mean if "If we substitute directly, the answer comes out to be D"
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Re: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)? &nbs [#permalink] 21 Oct 2017, 05:34
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