{[h(1)=0],[h(n)=h(n-1)-9]:} Find an explicit formula for h(n). h(n)=

Identify sequence type: Identify the type of sequence. The sequence is defined recursively, with each term being 9 less than the previous term. This indicates that it is an arithmetic sequence.Determine first term and common difference: Determine the first term and the common difference. The first term h(1) is given as 0, and the common difference is the amount subtracted from each term to get the next, which is -9.Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, which is h(n) = h(1) + (n-1)d, where h(1) is the first term and d is the common difference.Substitute values into formula: Substitute the values of h(1) and d into the formula. Since h(1) = 0 and d = -9, the formula becomes h(n) = 0 + (n-1)(-9).Simplify the expression: Simplify the expression. The formula simplifies to h(n) = -9(n-1).Distribute -9 within parentheses: Distribute the -9 within the parentheses to get the final explicit formula. The expression becomes h(n) = -9n + 9.

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{[h(1)=0],[h(n)=h(n-1)-9]:}
Find an explicit formula for
h(n).

h(n)=

$\left\{\begin{array}{l} h(1)=0 \\ h(n)=h(n-1)-9 \end{array}\right.$ $\newline$ Find an explicit formula for $h(n)$ . $\newline$ $h(n)=$

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Algebra 2

Write a formula for an arithmetic sequence

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\left\{\begin{array}{l} h(1)=0 \\ h(n)=h(n-1)-9 \end{array}\right.

\newline

Find an explicit formula for

h(n)

\newline

h(n)=

Identify sequence type: Identify the type of sequence. The sequence is defined recursively, with each term being $9$ less than the previous term. This indicates that it is an arithmetic sequence.
Determine first term and common difference: Determine the first term and the common difference. The first term $h(1)$ is given as $0$ , and the common difference is the amount subtracted from each term to get the next, which is $-9$ .
Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, which is $h(n) = h(1) + (n-1)d$ , where $h(1)$ is the first term and $d$ is the common difference.
Substitute values into formula: Substitute the values of $h(1)$ and $d$ into the formula. Since $h(1) = 0$ and $d = -9$ , the formula becomes $h(n) = 0 + (n-1)(-9)$ .
Simplify the expression: Simplify the expression. The formula simplifies to $h(n) = -9(n-1)$ .
Distribute $-9$ within parentheses: Distribute the $-9$ within the parentheses to get the final explicit formula. The expression becomes $h(n) = -9n + 9$ .