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Question

The Fibonacci sequence is defined by 1=a1=a2 and an=an1+an2,n>2
Find an+1an,for n=1,2,3,4,5

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Solution

1=a1=a2an=an1+an2,n>2a3=a2+a1=1+1=2a4=a3+a2=2+1=3a5=a4+a3=3+2=5a6=a5+a4=5+3=8
For n=1,an+1an=a2a1=11=1For n=2,an+1an=a3a2=21=2For n=3,an+1an=a4a3=32For n=4,an+1an=a5a4=53For n=5,an+1an=a6a5=85

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