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If f(1)=8 and f(n)=-5f(n-1)+2 then find the value of f(4) Answer:

If f(1)=8 f(1)=8 and f(n)=−5f(n−1)+2 f(n)=-5 f(n-1)+2 then find the value of f(4) f(4) \newlineAnswer:

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Q. If f(1)=8 f(1)=8 and f(n)=−5f(n−1)+2 f(n)=-5 f(n-1)+2 then find the value of f(4) f(4) \newlineAnswer:
  1. Find f(2)f(2): We are given that f(1)=8f(1) = 8. To find f(4)f(4), we need to find the values of f(2)f(2), f(3)f(3), and then f(4)f(4) using the recursive formula f(n)=−5f(n−1)+2f(n) = -5f(n-1) + 2.\newlineFirst, let's find f(2)f(2) using f(1)f(1).\newlinef(2)=−5f(1)+2f(2) = -5f(1) + 2\newlinef(1)=8f(1) = 800\newlinef(1)=8f(1) = 811\newlinef(1)=8f(1) = 822
  2. Find f(3)f(3): Now, let's find f(3)f(3) using f(2)f(2).
    f(3)=−5f(2)+2f(3) = -5f(2) + 2
    f(3)=−5(−38)+2f(3) = -5(-38) + 2
    f(3)=190+2f(3) = 190 + 2
    f(3)=192f(3) = 192
  3. Find f(4)f(4): Finally, we can find f(4)f(4) using f(3)f(3).
    f(4)=−5f(3)+2f(4) = -5f(3) + 2
    f(4)=−5(192)+2f(4) = -5(192) + 2
    f(4)=−960+2f(4) = -960 + 2
    f(4)=−958f(4) = -958

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