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

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New post 03 Jul 2016, 05:53
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:41) correct 12% (01:49) 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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Re: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?  [#permalink]

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New post 03 Jul 2016, 10:06
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
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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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New post 03 Jul 2016, 10:09
1
Solve to get:
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5

Hence, answer is 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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New post 04 Jul 2016, 23:31
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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New post 21 Oct 2017, 06:34
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, 06:34
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