h(n)=-31-7(n-1) Complete the recursive formula of h(n). {:[h(1)=◻],[h(n)=h(n-1)+]:}

Find First Term: Determine the first term of the sequence h(n). To find h(1), we substitute n = 1 into the given formula h(n) = -31 - 7(n - 1). h(1) = -31 - 7(1 - 1) h(1) = -31 - 7(0) h(1) = -31 - 0 h(1) = -31Calculate Difference: Find the difference between consecutive terms of the sequence. Since the sequence is defined by h(n) = -31 - 7(n - 1), we can see that the sequence decreases by 7 for each increase in n by 1. This is because the term -7(n - 1) decreases by 7 each time n increases by 1.Write Recursive Formula: Write the recursive formula using the first term and the common difference. The recursive formula for a sequence where each term is found by adding a constant difference to the previous term is given by: h(n) = h(n - 1) + d, where d is the common difference. Since the sequence decreases by 7, d = -7. Therefore, the recursive formula is: h(n) = h(n - 1) - 7

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h(n)=-31-7(n-1)
Complete the recursive formula of
h(n).

{:[h(1)=◻],[h(n)=h(n-1)+]:}

$h(n)=-31-7(n-1)$ $\newline$ Complete the recursive formula of $h(n)$ . $\newline$ $\begin{array}{l} h(1)=\square \\ h(n)=h(n-1)+\square \end{array}$

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Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

h(n)=-31-7(n-1)

\newline

Complete the recursive formula of

h(n)

\newline

\begin{array}{l} h(1)=\square \\ h(n)=h(n-1)+\square \end{array}

Find First Term: Determine the first term of the sequence $h(n)$ . To find $h(1)$ , we substitute $n = 1$ into the given formula $h(n) = -31 - 7(n - 1)$ . $h(1) = -31 - 7(1 - 1)$ $h(1) = -31 - 7(0)$ $h(1) = -31 - 0$ $h(1) = -31$
Calculate Difference: Find the difference between consecutive terms of the sequence. $\newline$ Since the sequence is defined by $h(n) = -31 - 7(n - 1)$ , we can see that the sequence decreases by $7$ for each increase in $n$ by $1$ . This is because the term $-7(n - 1)$ decreases by $7$ each time $n$ increases by $1$ .
Write Recursive Formula: Write the recursive formula using the first term and the common difference. $\newline$ The recursive formula for a sequence where each term is found by adding a constant difference to the previous term is given by: $\newline$ $h(n) = h(n - 1) + d$ , where $d$ is the common difference. $\newline$ Since the sequence decreases by $7$ , $d = -7$ . $\newline$ Therefore, the recursive formula is: $\newline$ $h(n) = h(n - 1) - 7$