Question

Find a formula for f(n) if f(0)=2, f(1)=5, f(2)=1, and for n≥3, f(n)=3f(n-1)-3f(n-2)+f(n-3).

Answer 1

If f(n) = -2f(n-1), and you need to evaluate f(5), then we need to look at the the function like this. f(5) = -2f(4)f(4) = -2f(3)f(3) = -2f(2)f(2) = -2f(1) Now, let's work this from the bottom upf(2) = -2f(1) = -2(3) = -6  since we are told that f(1) = 3f(3) = -2f(2) = -2(-6) = 12f(4) = -2f(3) = -2(12) =-24f(5) = -2f(4) = -2(-24) = 48