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{:[{[f(1)=-6],[f(2)=-4],[f(n)=f(n-2)+f(n-1)]:}],[f(3)=◻]:}

{f(1)=−6f(2)=−4f(n)=f(n−2)+f(n−1)f(3)= \begin{array}{l}\left\{\begin{array}{l}f(1)=-6 \\ f(2)=-4 \\ f(n)=f(n-2)+f(n-1)\end{array}\right. \\ f(3)=\end{array}

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Full solution

Q. {f(1)=−6f(2)=−4f(n)=f(n−2)+f(n−1)f(3)= \begin{array}{l}\left\{\begin{array}{l}f(1)=-6 \\ f(2)=-4 \\ f(n)=f(n-2)+f(n-1)\end{array}\right. \\ f(3)=\end{array}
  1. Given Recursive Function: We are given the following recursive function:\newlinef(1)=−6f(1) = -6\newlinef(2)=−4f(2) = -4\newlinef(n)=f(n−2)+f(n−1)f(n) = f(n-2) + f(n-1)\newlineWe need to find the value of f(3)f(3).
  2. Finding f(3)f(3): According to the recursive formula, f(3)f(3) can be found by adding f(1)f(1) and f(2)f(2).\newlineSo, f(3)=f(1)+f(2)f(3) = f(1) + f(2).
  3. Substituting Values: Substitute the given values into the equation:\newlinef(3)=f(1)+f(2)=(−6)+(−4)f(3) = f(1) + f(2) = (-6) + (-4).
  4. Performing Addition: Perform the addition to find f(3)f(3):f(3)=−6+(−4)=−10.f(3) = -6 + (-4) = -10.

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