2006-06-14 06:47:55 · 16 answers · asked by Kristine 1 in Science & Mathematics ➔ Mathematics
Every two numbers in the Fibonacci sequence is an even number, except at the beginning if you include 0. If you do include 0, then there is no pattern at all. I'm very confused right now.
2006-06-14 06:56:54 · update #1
Yes. Even if you define the sequence with F(1)=F(2)=1, you can still work backward to get
F(0)=0
F(-1)=1
F(-2)=-1
F(-3)=2
F(-4)=-3
The negative fibonacci sequence is identical to the positive one except that it alternates between positive and negative numbers. Also, every other number is not even, but every third number is even. If you define F(0)=0, F(1)=1, then look at every F(n) where n is a multiple of 3.
There's also an interesting equation that gives all values in the Fibonacci sequence, even the ones that aren't integers. I don't feel like typing it here (it wouldn't be readable anyway), but it's at http://en.wikipedia.org/wiki/Fibonacci_number#Closed_form_expression
2006-06-14 08:22:11 · answer #1 · answered by Anonymous · 1⤊ 2⤋
Yes it is.
Fibonacci numbers are formed by starting with 0 and 1 and then adding the latest two numbers to get the next one:
0 1 --the series starts like this.
0+1=1 so the series is now
0 1 1
1+1=2 so the series continues...
0 1 1 2 and the next term is
1+2=3 so we now have
0 1 1 2 3 and it continues as follows ...
2006-06-14 06:52:35 · answer #2 · answered by Hi 3 · 0⤊ 0⤋
Depends. The fist two numbers of the series are defined. Normally they are defined f(0)=0 and f(1)=1, so on most accounts: yes, 0 is a Fibonacci number.
2006-06-14 06:53:50 · answer #3 · answered by der_tabor 1 · 0⤊ 0⤋
through definition, the first 2 Fibonacci numbers are 0 and a million, and each and each most suitable volume is the sum of the previous 2. it truly is what makes those numbers area of the Fibonacci series. Have a sturdy day!
2016-10-30 21:33:26 · answer #4 · answered by Anonymous · 0⤊ 0⤋
the fibonacci sequence is defined as the numbers you get when add the two preceeding numbers. i.e. F(n)=F(n-1)+F(n-2).hence if we define F(0)=0 and F(1)=1 then zero can be included in the fibonacci sequence as we have defined it properly.
2006-06-14 06:59:36 · answer #5 · answered by poppy p 1 · 0⤊ 0⤋
If you start the series as 0 1 1 2 3..... then yes.
2006-06-14 06:51:03 · answer #6 · answered by ag_iitkgp 7 · 0⤊ 0⤋
The fibonacci sequence is defined as starting at 1.
F0 = 1
F1 = 1
F2 = 2
F3 = 3
etc.
So, if by "fibonacci number" you mean "is in the fibonacci sequence", then zero is not a fibonacci number.
2006-06-14 06:52:30 · answer #7 · answered by fatal_flaw_death 3 · 1⤊ 0⤋
no, its not, the sequence starts as follows:
1, 1, 2, 3, 5, 8, 13, 21, 34..and so on. By definition, it starts with two 1's
2006-06-14 06:51:26 · answer #8 · answered by Brian 3 · 0⤊ 0⤋
It can be, depending on your philosphy on numbers =).
If you start the sequence with a zero, and run it as
0,1,1,2,3,5,8,13 etc, it can be considered a fibonacci number. Often you will find the sequence defined in this exact manner.
HOWEVER..the status of zero as a 'number' and therefor valid to exist in the sequence- can be argued..
2006-06-14 06:59:36 · answer #9 · answered by DU|U 3 · 0⤊ 0⤋
U can choose yes and no.All numbers,except for indeterminates,are Fibonacci numbers.Including complex numbers.
2006-06-14 22:13:40 · answer #10 · answered by Kenneth Koh 5 · 0⤊ 0⤋