Question

\[\begin{cases} f(1)=-6 \\\\ f(2)=-4 \\\\ f(n)=f(n-2) + f(n-1) \end{cases}\] \[f(3)=\]

Answer 1

f(3) = -10

Explanation:

Given:

`\begin{cases} f(1)=-6 \\\\ f(2)=-4 \\\\ f(n)=f(n-2) + f(n-1) \end{cases}`

To find f(3), we can substitute n = 3 into the equation for f(n):

`f(3)=f(3-2)+f(3-1)`

Therefore:

`f(3)=f(1)+f(2)`

Substitute the given values of f(1) = -6 and f(2) = -4:

`f(3)=-6+(-4)`

`f(3)=-6-4`

`f(3)=-10`

Therefore, the value of f(3) is:

`\Large\boxed{\boxed{f(3)=-10}}`