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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)?

by Max@Math Revolution » Sun Jul 03, 2016 4:53 am
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

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by 800_or_bust » Sun Jul 03, 2016 9:56 am
Max@Math Revolution wrote: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.
A(1) = 1
A(2) = 1 + 1/(A(1)) = 1 + 1/1 = 2
A(3) = 1 + 1/(A(2)) = 1 + 1/2 = 3/2
A(4) = 1 + 1/(A(3)) = 1 + 1/(3/2) = 1 + 2/3 = 5/3
A(5) = 1 + 1/(A(4)) = 1 + 1/(5/3) = 1 + 3/5 = 8/5

Answer choice: D
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by Max@Math Revolution » Mon Jul 04, 2016 10:31 pm
If we substitute directly, the answer comes out to be D.
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