The function \(f(n) = 3f(n-2) - 2f(n-1)\), where \(f(2) = 3\) and \(f(1) = -1\) . What is the value of \(f(5)\)?

Guest Oct 28, 2019

#3**+1 **

I cant find the edit botton so ..

The function \(f(n) = 3f(n-2) - 2f(n-1) \) , where \(f(2) = 3\) and \(f(1) = -1\) . What is the value of \(f(5)\) ?

Is this any better ?

Tell me if not.

Guest Oct 29, 2019

#4**+2 **

f(5) = 3f(5-2) - 2f(5 - 1)

f(5) = 3f(3) - 2f(4)

f(5) = 3 [ 3f(3-2) - 2f(3 - 1) ] - 2 [ 3f(4-2) -2f(4 - 1)]

f(5) = 3 [ 3f(1) - 2f(2)] - 2[ 3f(2) - 2f(3) ]

f(5) = 3 [ 3(-1) - 2(3) ] - 2 [ 3(3) - 2f(3) ]

f(5) = 3[ -9] - 2 [ 9 ] + 4f(3)

f(5) = -45 + 4 [3f(3 - 2) - 2f(3 - 1)]

f(5) = -45 + 4 [ 3f(1) - 2f(2) ]

f(5) = -45 + 4 [ 3(-1) - 2(3) ]

f(5) = -45 +4 [ -3 - 6 ]

f(5) = -45 + 4 (-9)

f(5) = -45 - 36

f(5) = -81

CPhill Oct 29, 2019