Question

Fun\Interesting Problem, i'll post in a sec.

Answer 1

We know a recurrence formula for the Fibonacci sequence is
\[F_{n+2} = F_{n+1}+F_n\]
\[F_0 = 0, F_1 = 1\]
The sequence is 0, 1, 1, 2, 3, 5, 8, 13, ....
Can someone come up with a recurrence formula for every even Fibonacci number?

Answer 2

Can any one help me with my question???

Answer 3

　 ／l、
（ﾟ､ ｡ ７ This makes math kitty confused
　l、 ~ヽ
　じしf_, )ノ

Answer 4

that cat is awesome

Answer 5

hahaha thanks.. I messed the spacing up a bit on top >.<

Answer 6

lol >.> i guess i can be a little more specific. Im looking for something like:
\[G_{n+2} = aG_{n+1}+bG_n\]
where this formula fits the sequence:
0, 1, 3, 8, 21,...

Answer 7

So, We can not include odd terms in our Expression

Answer 8

i guess basically im looking for what numbers are a and b lol >.<

Answer 9

The Normal Sequence is \[0,1,1,2,3,5,8,13,21,34,...\]
Even Sequence \[2,8,34,...\]

Answer 10

Is it even term or even Places ?

Answer 11

oh my bad my bad, i dont mean the even terms like that. yes yes even places.

Answer 12

a=3
b=-1

Answer 13

too easy

Answer 14

Myininaya ftw! you just pop outta nowhere like a ninja lol

Answer 15

Ok then the Term are \[1,2,5,13,34,...\] Myininaya you did that too fast !

Answer 16

for even Fibonnaci series, as per formula you have mentioned , a=4 and b =1 .

Answer 17

all we need is some college algebra

Answer 18

wow chenna, thats a pretty cool relation, i hadnt seen that one before.

Answer 19

and joe im not really here
im here in spirit
just seen this question and i was like i have to answer this

Answer 20

hahaha

Answer 21

for even numbers in Fibinacci series 0,2,8,34,144,610,2584, ...
\[F _{n+2}=aF _{n+1}+bF _{n}\], a=4 and b=1, F0=0, F1=2. there you go. Please let me know if this is not what you expected.

Answer 22

it wasnt, i incorrectly expressed what i was looking for. I was looking for the even places:
\[F_0, F_2, F_4, \ldots\]
So its my bad.
But that recurrence you have is very interesting!

Answer 23

myininaya already got it. a=3 and b=-1 are the numbers you are looking for. Its not actually difficult to do so once you have the actual Fibonacci series. Because \[F _{n}\] \[n \ge 3\] are linear combinations of first 3 numbers namely 0,1,1. So what you have asked is very trivial.

Answer 24

and because i like to over complicate things heres how i would have solved it (for the even places)

Answer 25

yeah its too complicated. As I already know the series, I would generate two set of equations in a and b and solve them for a and b. Just linear algebra.
0*b+1*a=3 => a=3
1*b+3*3=8 => b=-1.
thats it. there you go.

Answer 26

While i admit it is complicated, it shows more about inner workings of the sequence than the algebraic method. Sometimes by taking the long path you see more~
lol

Answer 27

true math gurus

Answer 28

I don't get it myininaya your constantly viewing this question since morning ..is it something wrong in openstudy or you left your computer like this

Answer 29

Stalker^^

Answer 30

i left my computer like this
i told joe just before i left that i was only here in spirit (not really here)

Answer 31

im back now

Answer 32

im with malevolence on this one. stalker!!!