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{:[{[g(1)=-5],[g(2)=3]:}],[g(n)=g(n-2)+g(n-1)]:}

$\begin{array}{l}\left\{\begin{array}{l}g(1)=-5 \\ g(2)=3 \\ g(n)=g(n-2)+g(n-1)\end{array}\right. \\ g(3)=\square\end{array}$

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Evaluate recursive formulas for sequences

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Q.

\begin{array}{l}\left\{\begin{array}{l}g(1)=-5 \\ g(2)=3 \\ g(n)=g(n-2)+g(n-1)\end{array}\right. \\ g(3)=\square\end{array}

Given Information: We are given: $\newline$ g( $1$ ) = $-5$ $\newline$ g( $2$ ) = $3$ $\newline$ And the recursive formula: $\newline$ g(n) = g(n $-2$ ) + g(n $-1$ ) $\newline$ We need to find the value of g( $3$ ). $\newline$ Using the recursive formula, we substitute n with $3$ : $\newline$ g( $3$ ) = g( $3$ $-2$ ) + g( $3$ $-1$ ) $\newline$ g( $3$ ) = g( $1$ ) + g( $2$ ) $\newline$ g( $3$ ) = $-5$ + $3$ $\newline$ g( $3$ ) = $-2$
Finding $g(3)$ : Now we need to find the value of $g(4)$ . $\newline$ Using the recursive formula again, we substitute $n$ with $4$ : $\newline$ $g(4) = g(4-2) + g(4-1)$ $\newline$ $g(4) = g(2) + g(3)$ $\newline$ $g(4) = 3 + (-2)$ $\newline$ $g(4) = 1$

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