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sezza

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Fibonacci Sequence

What is the number before 4181 in the Fibonacci sequence. Explain how you could work this out without knowing all the numbers in the sequence

JohnnyReinB

Member

Registered: 2007-10-08

Posts: 453

Re: Fibonacci Sequence

Hmm, I'm thinking this has something to do with PHI...

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Fibonacci Sequence

One funny way is to add a zero to 4181 to make 41810.
Now start with this series: 0 10 10 20 30 50 80 130 210 340 550 890
1440
2330
3770
This number is overloading digits above 9 in the base-10 system:
5(10)(10)0 
8(17)(17)0
13(27)(27)0
21(44)(44)0
34(71)(71)0
Calculate this:
34000 + 7100 + 710 =
41100 + 710 =
41810
Yep!!  We did it without looking at
all of the numbers!!
Answer = 2100 + 440 + 44 = 2584

Also if you multiply 4181 by 0.618 you get just a tad under 2584,
and 0.618 and 1.618 are nearly reciprocals (golden ratio)
(√5 + 1)/2

Last edited by John E. Franklin (2008-02-15 18:31:54)

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