2. if $f(1)=4$ and $f(n)= - 3f(n - 1)$ then find the value of $f(6)$.

Explanation:

Step1: Find f(2)

Given $f(n)= - 3f(n - 1)$ and $f(1)=4$, then $f(2)=-3f(2 - 1)=-3f(1)=-3\times4=-12$.

Step2: Find f(3)

$f(3)=-3f(3 - 1)=-3f(2)=-3\times(-12) = 36$.

Step3: Find f(4)

$f(4)=-3f(4 - 1)=-3f(3)=-3\times36=-108$.

Step4: Find f(5)

$f(5)=-3f(5 - 1)=-3f(4)=-3\times(-108)=324$.

Step5: Find f(6)

$f(6)=-3f(6 - 1)=-3f(5)=-3\times324=-972$.

Answer:

$-972$