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If f(1)=2 and f(n)=4f(n-1)-n then find the value of f(3). Answer:

If f(1)=2 f(1)=2 and f(n)=4f(n−1)−n f(n)=4 f(n-1)-n then find the value of f(3) f(3) .\newlineAnswer:

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Q. If f(1)=2 f(1)=2 and f(n)=4f(n−1)−n f(n)=4 f(n-1)-n then find the value of f(3) f(3) .\newlineAnswer:
  1. Find f(2)f(2): We are given f(1)=2f(1) = 2. To find f(3)f(3), we first need to find f(2)f(2) using the recursive formula f(n)=4f(n−1)−nf(n) = 4f(n-1) - n.\newlineSubstitute n=2n = 2 into the formula to find f(2)f(2).\newlinef(2)=4f(2−1)−2f(2) = 4f(2-1) - 2\newlinef(2)=4f(1)−2f(2) = 4f(1) - 2\newlinef(2)=4(2)−2f(2) = 4(2) - 2\newlinef(1)=2f(1) = 200\newlinef(1)=2f(1) = 211
  2. Calculate f(3)f(3): Now that we have f(2)=6f(2) = 6, we can find f(3)f(3) using the same recursive formula.\newlineSubstitute n=3n = 3 into the formula to find f(3)f(3).\newlinef(3)=4f(3−1)−3f(3) = 4f(3-1) - 3\newlinef(3)=4f(2)−3f(3) = 4f(2) - 3\newlinef(3)=4(6)−3f(3) = 4(6) - 3\newlinef(3)=24−3f(3) = 24 - 3\newlinef(3)=21f(3) = 21

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