If f(1) = 3 and f(n) = -2f(n - 1) + 1, then f(5) =
(1) -5 (3) 21
(2) 11 (4) 43

F(1) = 3
(when you put 1 into the function, you get 3)
f(n) = -2f(n-1) + 1
(this is how the function works with any number n...
the f(n-1) means putting a number 1 lower into the function...
of course this keeps going until you get f(1) = 3)

We want to find f(5), which is what you get when you plug in 5.
Let's plug 5 into that function!

f(5) = -2f(5-1) + 1
we need to find f(4)
f(4) = -2f(4-1) + 1
we need to find f(3)...
f(3) = -2f(3-1) + 1
we need to find f(2)
f(2) = -2f(2-1) + 1
we know that f(1) = 3...
f(2) = -2(3) + 1 = -6 + 1 = -5
we can plug f(2) = -5 into f(3)
f(3) = -2(-5) + 1 = 10 + 1 = 11
we can plug f(3) = 11 into f(4)
f(4) = -2(11) + 1 = -22 + 1 = -21
we can plug f(4) = -21 into f(5)
f(5) = -2(-21) + 1 = 42 + 1 = 43