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

Question Prompt: The question prompt is asking us to find the value of f(2) given the recursive function f(n) = 2*f(n-1) + 1 with the initial condition f(1) = -3.Initial Condition: We know that f(1) = -3. To find f(2), we use the recursive formula f(n) = 2*f(n-1) + 1 with n = 2.Recursive Formula: Substitute n = 2 into the recursive formula to get f(2) = 2*f(2-1) + 1.Substitute n = 2: Calculate f(2) using the value of f(1): f(2) = 2*f(1) + 1 = 2*(-3) + 1.Calculate f(2): Perform the multiplication and addition: f(2) = 2*(-3) + 1 = -6 + 1.Perform Multiplication and Addition: Simplify the result to get the final value of f(2): f(2) = -6 + 1 = -5.

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$\begin{array}{l}\left\{\begin{array}{l}f(1)=-3 \\ f(n)=2 \cdot f(n-1)+1\end{array}\right. \\ f(2)=\square\end{array}$

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Algebra 1

Evaluate recursive formulas for sequences

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

Question Prompt: The question prompt is asking us to find the value of $f(2)$ given the recursive function $f(n) = 2 \cdot f(n-1) + 1$ with the initial condition $f(1) = -3$ .
Initial Condition: We know that $f(1) = -3$ . To find $f(2)$ , we use the recursive formula $f(n) = 2 \cdot f(n-1) + 1$ with $n = 2$ .
Recursive Formula: Substitute $n = 2$ into the recursive formula to get $f(2) = 2 \cdot f(2-1) + 1$ .
Substitute $n = 2$ : Calculate $f(2)$ using the value of $f(1)$ : $f(2) = 2 \cdot f(1) + 1 = 2 \cdot (-3) + 1$ .
Calculate $f(2)$ : Perform the multiplication and addition: $f(2) = 2 \cdot (-3) + 1 = -6 + 1$ .
Perform Multiplication and Addition: Simplify the result to get the final value of $f(2)$ : $f(2) = -6 + 1 = -5$ .