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{[g(1)=5],[g(n)=-1*g(n-1)-4]:}

g(2)=

{g(1)=5g(n)=1g(n1)4g(2)= \begin{array}{l}\left\{\begin{array}{l}g(1)=5 \\ g(n)=-1 \cdot g(n-1)-4\end{array}\right. \\ g(2)=\square\end{array}

Full solution

Q. {g(1)=5g(n)=1g(n1)4g(2)= \begin{array}{l}\left\{\begin{array}{l}g(1)=5 \\ g(n)=-1 \cdot g(n-1)-4\end{array}\right. \\ g(2)=\square\end{array}
  1. Given initial condition and recursive formula: We are given the initial condition and the recursive formula for the function g(n)g(n):g(1)=5g(1) = 5g(n)=1×g(n1)4g(n) = -1 \times g(n - 1) - 4To find g(2)g(2), we need to use the value of g(1)g(1) in the recursive formula.
  2. Substitute n=2 n = 2 into recursive formula: Substitute n=2 n = 2 into the recursive formula to find g(2) g(2) :
    g(2)=1×g(21)4 g(2) = -1 \times g(2 - 1) - 4
    g(2)=1×g(1)4 g(2) = -1 \times g(1) - 4
    Now we use the initial condition g(1)=5 g(1) = 5 .
  3. Use initial condition g(1)=5g(1) = 5: Perform the substitution and calculation:\newlineg(2)=1×54g(2) = -1 \times 5 - 4\newlineg(2)=54g(2) = -5 - 4\newlineg(2)=9g(2) = -9

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