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If f(1)=7 and f(n)=4f(n-1)+n then find the value of f(3). Answer:

If f(1)=7 f(1)=7 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)=7 f(1)=7 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. Given f(1)=7f(1) = 7: We are given that f(1)=7f(1) = 7. 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(7)+2f(2) = 4(7) + 2\newlinef(1)=7f(1) = 700\newlinef(1)=7f(1) = 711
  2. Find f(2)f(2): Now that we have f(2)=30f(2) = 30, we can use it to 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(30)+3f(3) = 4(30) + 3\newlinef(3)=120+3f(3) = 120 + 3\newlinef(3)=123f(3) = 123

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