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

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

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Q. If f(1)=2 f(1)=2 and f(n)=−3f(n−1)+n f(n)=-3 f(n-1)+n then find the value of f(4) f(4) .\newlineAnswer:
  1. Given f(1)f(1): We are given that f(1)=2f(1) = 2. 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)=−3f(n−1)+nf(n) = -3f(n-1) + n.
  2. Find f(2)f(2): First, let's find f(2)f(2) using the formula:\newlinef(2)=−3f(2−1)+2f(2) = -3f(2-1) + 2\newlinef(2)=−3f(1)+2f(2) = -3f(1) + 2\newlinef(2)=−3(2)+2f(2) = -3(2) + 2\newlinef(2)=−6+2f(2) = -6 + 2\newlinef(2)=−4f(2) = -4
  3. Find f(3)f(3): Next, we find f(3)f(3) using the formula and the value of f(2)f(2) we just found:\newlinef(3)=−3f(3−1)+3f(3) = -3f(3-1) + 3\newlinef(3)=−3f(2)+3f(3) = -3f(2) + 3\newlinef(3)=−3(−4)+3f(3) = -3(-4) + 3\newlinef(3)=12+3f(3) = 12 + 3\newlinef(3)=15f(3) = 15
  4. Find f(4)f(4): Finally, we find f(4)f(4) using the formula and the value of f(3)f(3):
    f(4)=−3f(4−1)+4f(4) = -3f(4-1) + 4
    f(4)=−3f(3)+4f(4) = -3f(3) + 4
    f(4)=−3(15)+4f(4) = -3(15) + 4
    f(4)=−45+4f(4) = -45 + 4
    f(4)=−41f(4) = -41

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