Question

let g(x) be a function satisfying g(0)=2, g(1)=3, g(x+2)=2g(x) - g(x+1), then find out g(5)

Answer 1

g(x+2)=2g(x) - g(x+1)
Putting x=0
g(0+2)=2g(0) - g(0+1)
g(2)=2g(0) - g(1)
g(2)=2*2 - 3 (because g(0)=2, g(1)=3 )
g(2) = 1

g(x+2)=2g(x) - g(x+1)
Putting x=1
g(1+2)=2g(1) - g(1+1)
g(3) = 2*3 - 1 (because g(1)=3, g(2)=1 )
g(3)=5

g(x+2)=2g(x) - g(x+1)
Putting x=2
g(2+2)=2g(2) - g(2+1)
g(4) = 2*1 - 5 (because g(2)=1, g(3)=5 )
g(4)= -3

g(x+2)=2g(x) - g(x+1)
Putting x=3
g(3+2)=2g(3) - g(3+1)
g(5) = 2*5 - (-3) (because g(3)=5, g(4)=-3 )
g(5)=13

So, we got the value of g(5)=13