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)?
+9466 f(n) = 3f(n - 2) - 2f(n - 1) If we plug in 5 for n we get...
f(5) = 3f(5 - 2) - 2f(5 - 1) = 3f(3) - 2f(4)
Now lets work on finding f(3) and f(4)
We're given:
f(1) = -1
f(2) = 3
To find f(3) , plug in 3 for n into the function:
f(n) = 3f(n - 2) - 2f(n - 1)
f(3) = 3f(3 - 2) - 2f(3 - 1)
f(3) = 3f( 1 ) - 2f( 2 ) We know f(1) = -1 and f(2) = 3 so we can say...
f(3) = 3( -1 ) - 2( 3 )
f(3) = -9
To find f(4) , plug in 4 for n into the function:
f(n) = 3f(n - 2) - 2f(n - 1)
f(4) = 3f(4 - 2) - 2f(4 - 1)
f(4) = 3f( 2 ) - 2f( 3 ) We know f(2) = 3 and f(3) = -9 so we can say...
f(4) = 3( 3 ) - 2( -9 )
f(4) = 27
Now that we know f(3) = -9 and f(4) = 27 we can find f(5):
f(n) = 3f(n - 2) - 2f(n - 1)
f(5) = 3f(5 - 2) - 2f(5 - 1)
f(5) = 3f( 3 ) - 2f( 4 ) We know f(3) = -9 and f(4) = 27 so we can say...
f(5) = 3( -9 ) - 2( 27 )
f(5) = -81
+26367 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)?
\(\begin{array}{|rcll|} \hline \mathbf{f(n)} &=& \mathbf{(-1)^n*3^{n-1}} \\\\ f(5) &=& (-1)^5*3^{5-1} \\ f(5) &=& -3^4 \\ \mathbf{f(5)} &=& \mathbf{-81} \\ \hline \end{array}\)
