Answer:
f(4) = -55
Step-by-step explanation:
Given
f(1) = 5
f(n) = -2f(n-1) - 5
If you substitute n with 4 you get:
f(n) = -2f(n-1) - 5
f(4) = -2f(4-1) - 5
= -2f(3) - 5
This shows that you have to calculate the value of f(3) before we can get the value of f(4). To calculate f(3) we have to know f(2) and to calculate f(2) we have to know f(1), which is given.
Let's start from the bottom.
f(1) = 5
f(2) = -2f(n-1) - 5
= -2f(2-1) - 5
= -2f(1) - 5 // substitute f(1) with the value 5 (given)
= -2(5) - 5
= -15
f(3) = -2f(n-1) - 5
= -2f(3-1) - 5
= -2f(2) - 5
= -2(-15) - 5
= 25
Now we can finally calculate f(4)!
f(4) = -2f(n-1) - 5
= -2f(4-1) - 5
= -2f(3) - 5
= -2(25) - 5
= -55
