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Sunday, November 27, 2005 - 10:03 AM
In the Fibonacci sequence, if you take any three consecutive numbers, add them, and divide the sum by 2, you always get the third number. If this is confusing, let me explain:
1+2+3=6 and 6/2=3
5+8+13=26 and 26/2=13
21+34+55=110 and 110/2=55
89+144+233=466 and 466/2=233
377+610+987=1974 and 1974/2=987
and I assume it goes on to infinity.
-Rajan
1+2+3=6 and 6/2=3
5+8+13=26 and 26/2=13
21+34+55=110 and 110/2=55
89+144+233=466 and 466/2=233
377+610+987=1974 and 1974/2=987
and I assume it goes on to infinity.
-Rajan
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Comments
Oops - I should've read the thread before commenting. My apologies :)
Basically you have three numbers, x, y, z.
Because of how the Fibonacci sequence works x+y=z
When you add all three and divide by 2 you get
(x+y+z)/2
Basic substitution yields:
(z+z)/2 ; because x+y=z
which gives 2z/2 which equals z
So you didn't really prove anything but it's still a cool reworking of how the Fibonacci Sequence works.
so if any number in it = the sum of the two before it then if x, y, z are consecutive numbers of the sequence and x + y = z then x + y +z = z + z = 2z and 2z/2 = z
oops i kinda said the same thing as the ppl before me, sorry, should have read yours first
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