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# Writing and Using Explicit Rules for Arithmetic Sequences

## Writing and Using Explicit Rules for Arithmetic Sequences 1.13 - Solution

Let's visualize the information we have been given. We notice that the numbers are getting lower, so the common difference has to be a negative number. $\begin{gathered} 28 \ \stackrel{+\, d}{\rightarrow} \ 20 \ \stackrel{+\,d}{\rightarrow} \ 12 \ \stackrel{+\,d}{\rightarrow} \ 4 \end{gathered}$ The common difference of the arithmetic sequence can be determined by subtracting one of the terms from the next. Let's subtract the first term from the second term. $\begin{gathered} a_2-a_1=20-28=\text{-} 8 \end{gathered}$ Knowing the common difference, we should subtract $8$ from $28$ enough times until we end up at $\text{-} 36.$ If we call this number of times $n$, we get the following equation. $\begin{gathered} 28-8n=\text{-} 36 \end{gathered}$ Let's solve for $n.$
$28-8n=\text{-} 36$
$\text{-} 8n=\text{-} 64$
$n=8$
The eight term is $\text{-} 36.$