{:[{[h(1)=9],[h(n)=h(n-1)*(1)/(9)]:}],[h(3)=◻]:}

Recursive formula and initial condition: The question prompt is asking for the value of h(3) given the recursive formula h(n) = h(n-1) * (1/9) and the initial condition h(1) = 9.Finding the value of h(2): First, we need to find the value of h(2) using the recursive formula and the initial condition. h(n) = h(n-1) * (1/9) h(2) = h(1) * (1/9) h(2) = 9 * (1/9) h(2) = 1 We have found that h(2) = 1.Finding the value of h(3): Now, we can find the value of h(3) using the value of h(2) we just found. h(n) = h(n-1) * (1/9) h(3) = h(2) * (1/9) h(3) = 1 * (1/9) h(3) = 1/9 We have found that h(3) = 1/9.

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{:[{[h(1)=9],[h(n)=h(n-1)*(1)/(9)]:}],[h(3)=◻]:}

$\begin{array}{l}\left\{\begin{array}{l}h(1)=9 \\ h(n)=h(n-1) \cdot \frac{1}{9}\end{array}\right. \\ h(3)=\square\end{array}$

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Algebra 1

Evaluate recursive formulas for sequences

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\begin{array}{l}\left\{\begin{array}{l}h(1)=9 \\ h(n)=h(n-1) \cdot \frac{1}{9}\end{array}\right. \\ h(3)=\square\end{array}

Recursive formula and initial condition: The question prompt is asking for the value of $h(3)$ given the recursive formula $h(n) = h(n-1) \times \left(\frac{1}{9}\right)$ and the initial condition $h(1) = 9$ .
Finding the value of $h(2)$ : First, we need to find the value of $h(2)$ using the recursive formula and the initial condition. $\newline$ $h(n) = h(n-1) \times \left(\frac{1}{9}\right)$ $\newline$ $h(2) = h(1) \times \left(\frac{1}{9}\right)$ $\newline$ $h(2) = 9 \times \left(\frac{1}{9}\right)$ $\newline$ $h(2) = 1$ $\newline$ We have found that $h(2) = 1$ .
Finding the value of h( $3$ ): Now, we can find the value of h( $3$ ) using the value of h( $2$ ) we just found. $\newline$ h(n) = h(n $-1$ ) $\times$ $\frac{1}{9}$ $\newline$ h( $3$ ) = h( $2$ ) $\times$ $\frac{1}{9}$ $\newline$ h( $3$ ) = $1 \times \frac{1}{9}$ $\newline$ h( $3$ ) = $\frac{1}{9}$ $\newline$ We have found that h( $3$ ) = $\frac{1}{9}$ .