Answer:
f(4) = 59
Step-by-step explanation:
Given:
f(1) = 3
f(n) = f(n-1)2 + 5
Idea:
We want to find the value of f(4), so let's substitute n with 4.
f(n) = f(n-1)2 + 5
f(4) = f(4-1)2 + 5
f(4) = f(3)2 + 5
We see that we have to evaluate f(3) before we can calculate f(4).
So let's try to calculate f(3).
f(3) = f(3-1)2 + 5
f(3) = f(2)2 + 5
Again we have to calculate f(2) before we can calculate f(3). So what do we do?
Calculations:
The best approach is to start from the bottom. First let calculate the value of f(2) and then f(3) and finally f(4).
f(1) = 3 (this was given)
f(2) = f(2-1)2 + 5
= f(1)2 + 5 (this time we know the value of f(1)!)
= 3 × 2 + 5
= 6 + 5
= 11
f(3) = f(3-1)2 + 5
= f(2)2 + 5 (we calculated f(2) in the previous step: f(2) = 11)
= 11 × 2 + 5
= 22 + 5
= 27
f(4) = f(4-1)2 + 5
= f(3)2 + 5
= 27 × 2 + 5
= 51 + 5
= 59
