Writing and Using Explicit Rules for Arithmetic Sequences

To begin, let's observe the given terms in the sequence to determine the value of the first term as well as the common difference. $$\begin{array}{c}\text{-}1\stackrel{+0.5}{\to }\text{-}0.5\stackrel{+0.5}{\to }0\stackrel{+0.5}{\to }0.5\end{array}$$ As we can see $d=0.5$ and $a_1=\text{-}1.$ We can use this information to write an equation for the $n^{\text{th}}$ term of the sequence. We can calculate the fifth term of the sequence, $a_5$, by substituting $n=5$ into our equation.

Graphing the Sequence

When graphing a sequence, the $x\text{-}$axis always represents the number of the term $n$ and the $y\text{-}$axis represents the value of the term $a_n.$

$n$	$0.5n-1.5$	$a_n$	$(n,a_n)$
$1$	$0.5(1)-1.5$	$\text{-}1$	$(1,\text{-}1)$
$2$	$0.5(2)-1.5$	$\text{-}0.5$	$(2,\text{-}0.5)$
$3$	$0.5(3)-1.5$	$0$	$(3,0)$
$4$	$0.5(4)-1.5$	$0.5$	$(4,0.5)$
$5$	$0.5(5)-1.5$	$1$	$(5,1)$

Now let's graph these points on a coordinate plane.