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

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

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Q. If f(1)=4 f(1)=4 and f(n)=−2f(n−1) f(n)=-2 f(n-1) then find the value of f(4) f(4) .\newlineAnswer:
  1. Find f(2)f(2): We are given that f(1)=4f(1) = 4. To find f(4)f(4), we need to apply the recursive formula f(n)=−2f(n−1)f(n) = -2f(n-1) three times, starting with n=2n=2 and using the value of f(1)f(1).\newlineFirst, let's find f(2)f(2).\newlinef(2)=−2f(2−1)f(2) = -2f(2-1)\newlinef(2)=−2f(1)f(2) = -2f(1)\newlinef(2)=−2(4)f(2) = -2(4)\newlinef(1)=4f(1) = 400
  2. Find f(3)f(3): Now, let's find f(3)f(3) using the value of f(2)f(2).\newlinef(3)=−2f(3−1)f(3) = -2f(3-1)\newlinef(3)=−2f(2)f(3) = -2f(2)\newlinef(3)=−2(−8)f(3) = -2(-8)\newlinef(3)=16f(3) = 16
  3. Find f(4)f(4): Finally, we find f(4)f(4) using the value of f(3)f(3).
    f(4)=−2f(4−1)f(4) = -2f(4-1)
    f(4)=−2f(3)f(4) = -2f(3)
    f(4)=−2(16)f(4) = -2(16)
    f(4)=−32f(4) = -32

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