SOLUTION: If 𝑓(1) = 3 and 𝑓(𝑛) = −2𝑓(𝑛 − 1) + 1, then 𝑓(5) = A. -5 B. 11 C. 21 D. 43

Question 1173686: If 𝑓(1) = 3 and 𝑓(𝑛) = −2𝑓(𝑛 − 1) + 1,
then 𝑓(5) =
A. -5
B. 11
C. 21
D. 43
Answer by mila nedic(19) (Show Source): You can put this solution on YOUR website!
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.

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