if f(1)=3 and f(n)= -2f(n-1)+1 , then F(5)=

Question

I need to find what f(5)=

Answer 1

One way to solve this problem is to go step by step. 

 

The problem gives us f(1) = 3. 

 

f(n-1) means that we need to know the step before to calculate the next step. Fortunately for f(2) we know what that is. See above.

 

f(2) = -2 * f(1) +1 

 

When we subsitute f(1) for 3 we find straightforwardly that f(2) = -5

 

Keep repeating this procedure to find f(5)

 

f(3) = -2 * f(2) +2

 

f(4) = -2 * f(3) +2

 

f(5) = -2 * f(4) +2

 

Obviously this strategy wouldn't work for f(1000000000000) We'd need to figure out the pattern and apply it. I think solving these problems sequentially can be important to grasp what the notation f(n) is asking us to do. This is also the same logic that will be applied to graphing equations.

Answer 2

f(1)=3, f(n)=-2f(n-1)+1, f(5)=?

f(2)=-2f(2-1)+1=-2f(1)+1=-2(3)+1=-6+1=-5

f(2)=-5

f(3)=-2f(3-1)+1=-2f(2)+1=-2(-5)+1=10+1=11

f(3)=11

f(4)=-2(f4-1)+1=-2f(3)+1=-2(11)+1=-22+1=-21

f(4)=-21

f(5)=-2f(5-1)+1=-2f(4)+1=-2(-21)+1=42+1=43

f(5)=43