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Writing and Using Explicit Rules for Arithmetic Sequences

Writing and Using Explicit Rules for Arithmetic Sequences 1.13 - Solution

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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. 28 +d 20 +d 12 +d 4\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. a2a1=2028=-8\begin{gathered} a_2-a_1=20-28=\text{-} 8 \end{gathered} Knowing the common difference, we should subtract 88 from 2828 enough times until we end up at -36.\text{-} 36. If we call this number of times nn, we get the following equation. 288n=-36\begin{gathered} 28-8n=\text{-} 36 \end{gathered} Let's solve for n.n.
288n=-3628-8n=\text{-} 36
-8n=-64\text{-} 8n=\text{-} 64
The eight term is -36.\text{-} 36.