{[h(1)=96],[h(n)=h(n-1)-1]:} 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 one 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 96, and the common difference is the amount subtracted from each term to get the next term, which is -1.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 the formula: Substitute the values of h(1) and d into the formula. The first term h(1) is 96, and the common difference d is -1. So the explicit formula is h(n) = 96 + (n-1)(-1).Simplify the expression: Simplify the expression. h(n) = 96 - (n - 1) = 96 - n + 1 = 97 - n.

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{[h(1)=96],[h(n)=h(n-1)-1]:}
Find an explicit formula for
h(n).

h(n)=

$\left\{\begin{array}{l} h(1)=96 \\ h(n)=h(n-1)-1 \end{array}\right.$ $\newline$ 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)=96 \\ h(n)=h(n-1)-1 \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 one 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 $96$ , and the common difference is the amount subtracted from each term to get the next term, which is $-1$ .
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 the formula: Substitute the values of $h(1)$ and $d$ into the formula. The first term $h(1)$ is $96$ , and the common difference $d$ is $-1$ . So the explicit formula is $h(n) = 96 + (n-1)(-1)$ .
Simplify the expression: Simplify the expression. $h(n) = 96 - (n - 1) = 96 - n + 1 = 97 - n$ .