Writing and Using Explicit Rules for Arithmetic Sequences

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 $n.$ The eight term is $\text{-} 36.$