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If f(1)=8 and f(n)=-5f(n-1)-n then find the value of f(3). Answer:

If f(1)=8 f(1)=8 and f(n)=−5f(n−1)−n f(n)=-5 f(n-1)-n then find the value of f(3) f(3) .\newlineAnswer:

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Q. If f(1)=8 f(1)=8 and f(n)=−5f(n−1)−n f(n)=-5 f(n-1)-n then find the value of f(3) f(3) .\newlineAnswer:
  1. Find f(2)f(2): To find f(3)f(3), we need to first find f(2)f(2) using the recursive formula f(n)=−5f(n−1)−nf(n)=-5f(n-1)-n, with n=2n=2 and the known value f(1)=8f(1)=8.
    f(2)=−5f(1)−2f(2) = -5f(1) - 2
    f(2)=−5(8)−2f(2) = -5(8) - 2
    f(2)=−40−2f(2) = -40 - 2
    f(2)=−42f(2) = -42
  2. Find f(3)f(3): Now that we have f(2)f(2), we can find f(3)f(3) using the same recursive formula with n=3n=3.
    f(3)=−5f(2)−3f(3) = -5f(2) - 3
    f(3)=−5(−42)−3f(3) = -5(-42) - 3
    f(3)=210−3f(3) = 210 - 3
    f(3)=207f(3) = 207

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