Question 1173686
𝑓(𝑛) = −2𝑓(𝑛 − 1) + 1
𝑓(5) =
All we have to do here is to replace each n with 5 and continue until we get to 𝑓(1) which we know is 3.
𝑓(5) = −2𝑓(5 − 1) + 1
     =-2𝑓(4)+1    (now we need to figure out 𝑓(4)
𝑓(4)=−2𝑓(4 − 1) + 1
    =-2𝑓(3)+1  (now we need 𝑓(3)
𝑓(3)=−2𝑓(3 − 1) + 1
    =-2𝑓(2)+1   (now we need 𝑓(2)
𝑓(2)=−2𝑓(2 − 1) + 1
    =-2𝑓(1)+1  
    =-2(3)+1   (we can replace 𝑓(1) with 3 because we know they are equal)
    =-5     (𝑓(2) is -5 so now we go back up until we get to 𝑓(5))

𝑓(3)=−2𝑓(3 − 1) + 1
    =-2𝑓(2)+1
    =-2(-5)+1 (we can replace 𝑓(2) with -5 since we solved that in the last step) 
    =11
𝑓(4)=−2𝑓(4 − 1) + 1
    =-2𝑓(3)+1 
    =-2(11)+1 (we can replace 𝑓(3) with 11)
    =-21
𝑓(5) = −2𝑓(5 − 1) + 1
     =-2𝑓(4)+1 
     =-2(-21)+1 (we can replace 𝑓(4) with -21)
     =43 (𝑓(5) is 43)

Therefore 𝑓(5) is equal to D. 43.