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{[f(1)=-7],[f(n)=f(n-1)+3.5]:} f(3)=

{f(1)=−7f(n)=f(n−1)+3.5f(3)=□ \begin{array}{l}\left\{\begin{array}{l}f(1)=-7 \\ f(n)=f(n-1)+3.5\end{array}\right. \\ f(3)=\square\end{array}

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Full solution

Q. {f(1)=−7f(n)=f(n−1)+3.5f(3)=□ \begin{array}{l}\left\{\begin{array}{l}f(1)=-7 \\ f(n)=f(n-1)+3.5\end{array}\right. \\ f(3)=\square\end{array}
  1. Given initial condition and recursive formula: We are given the initial condition and the recursive formula:\newlinef(11) = −7-7\newlinef(n) = f(n−1-1) + 3.53.5\newlineTo find f(33), we first need to find f(22).
  2. Calculating f(2)f(2) using the recursive formula: Using the recursive formula, we calculate f(2)f(2):
    f(2)=f(1)+3.5f(2) = f(1) + 3.5
    f(2)=−7+3.5f(2) = -7 + 3.5
    f(2)=−3.5f(2) = -3.5
  3. Calculating f(3)f(3) using the value of f(2)f(2): Now we use the value of f(2)f(2) to find f(3)f(3):
    f(3)=f(2)+3.5f(3) = f(2) + 3.5
    f(3)=−3.5+3.5f(3) = -3.5 + 3.5
    f(3)=0f(3) = 0

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