TCS - given g(0)=1,g(1)=-1and g(n)=g(n-1)+g(n-2),find(6).

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given g(0)=1,g(1)=-1and g(n)=g(n-1)+g(n-2),find(6).

Total Answers and Comments: 3

Last Update: February 27, 2008 Asked by: ramesh

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Best Rated Answer

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Submitted by: abhishek76

we can write g(6) as g(5)+g(4) (since g(n)=g(n-1)+g(n-2))
again g(5)=g(4)+g(3),
          g(4)=g(3)+g(2)
          g(3)=g(2)+g(1)
          g(2)=g(1)+g(0)=1-1=0(as given above)
     therefore,g(3)= 0-1=-1
                     g(4)=-1+0=-1
                     g(5)=-1-1=-2
   therefore, g(6)=g(5)+g(4)=-2-1=-3(ans)

Above answer was rated as good by the following members:
yoooooooooo

October 23, 2007 01:56:58

santosh

RE: given g(0)=1,g(1)=-1and g(n)=g(n-1)+g(n-2),find(6)...

# substitute n 6

> g(6) g(5)+g(4)----------------(1)
# sub n 5
> g(5) g(4)+g(3)-----------------(2)

# sub n 4
> g(4) g(3)+g(2)------------------(3)
#sub n 3
> g(3) g(2)+g(1)--------------------(4)
# sub n 2
> g(2) g(1)+g(0)--------------------(5)

so
g(2) 0;
g(3) -1;
g(4) -1;
g(5) -2;

g(6) -3;

another method:

g(6) 5*g(1)+g(0)

so generalised solution is g(a) (a-1)*g(1) + g(o) where a is to find for the given equation g(n) g(n-1)+g(n-2)

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February 25, 2008 02:35:00

abhishek76

Member Since: February 2008 Contribution: 1

RE: given g(0)=1,g(1)=-1and g(n)=g(n-1)+g(n-2),find(6).

we can write g(6) as g(5)+g(4) (since g(n) g(n-1)+g(n-2))
again g(5) g(4)+g(3)
g(4) g(3)+g(2)
g(3) g(2)+g(1)
g(2) g(1)+g(0) 1-1 0(as given above)
therefore g(3) 0-1 -1
g(4) -1+0 -1
g(5) -1-1 -2
therefore g(6) g(5)+g(4) -2-1 -3(ans)

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February 27, 2008 18:45:43

vigneshkumar1988

Member Since: February 2008 Contribution: 7

RE: given g(0)=1,g(1)=-1and g(n)=g(n-1)+g(n-2),find(6).

g(6) g(5)+g(4)
now we dont know about g(5) g(4)
g(5) g(4)+g(3)
g(4) g(3)+g(2)
g(3) g(2)+g(1)
g(2) G(1)+g(0)

now on solving
g(2) -1
g(3) -2
g(4) -3
g(5) -5
g(6) -8

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