{[h(1)=-75],[h(n)=h(n-1)-10]:} 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 10 less than the previous term, which 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 -75. The common difference, d, is the amount subtracted from each term to get the next term, which is -10.Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, which is h(n) = h(1) + (n-1)d. Substitute the values of h(1) and d into the formula. The explicit formula for the sequence is h(n) = -75 + (n-1)(-10).Simplify the formula: Simplify the formula. Distribute the -10 inside the parentheses to get h(n) = -75 - 10(n-1). This simplifies to h(n) = -75 - 10n + 10, which further simplifies to h(n) = -10n - 65.

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{[h(1)=-75],[h(n)=h(n-1)-10]:}
Find an explicit formula for
h(n).

h(n)=

$\left\{\begin{array}{l} h(1)=-75 \\ h(n)=h(n-1)-10 \end{array}\right.$ $\newline$ 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)=-75 \\ h(n)=h(n-1)-10 \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 $10$ less than the previous term, which 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 $-75$ . The common difference, $d$ , is the amount subtracted from each term to get the next term, which is $-10$ .
Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, which is $h(n) = h(1) + (n-1)d$ . Substitute the values of $h(1)$ and $d$ into the formula. The explicit formula for the sequence is $h(n) = -75 + (n-1)(-10)$ .
Simplify the formula: Simplify the formula. Distribute the $-10$ inside the parentheses to get $h(n) = -75 - 10(n-1)$ . This simplifies to $h(n) = -75 - 10n + 10$ , which further simplifies to $h(n) = -10n - 65$ .