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{f(1)=3 f(n)=2f(n1)+1\begin{cases} f(1)=-3 \ f(n)=2\cdot f(n-1)+1 \end{cases}, f(2)=f(2)=

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Q. {f(1)=3 f(n)=2f(n1)+1\begin{cases} f(1)=-3 \ f(n)=2\cdot f(n-1)+1 \end{cases}, f(2)=f(2)=
  1. Find f(2) f(2) : \newlineFirst, we need to find f(2) f(2) using the given recursive formula. We know f(1)=3 f(1) = -3 .
  2. Use Recursive Formula: \newlineThe formula given is f(n)=2f(n1)+1 f(n) = 2 \cdot f(n-1) + 1 . So, let's plug in n=2 n = 2 . \newlinef(2)=2f(1)+1 f(2) = 2 \cdot f(1) + 1
  3. Substitute f(1) f(1) : Substitute f(1)=3 f(1) = -3 into the equation: f(2)=2×(3)+1 f(2) = 2 \times (-3) + 1
  4. Calculate: \newlineCalculate: \newlinef(2)=6+1=5 f(2) = -6 + 1 = -5

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