Answer
$a_{n}=5n-28$
.
Work Step by Step
If the sequence is arithmetic, the general rule is
$ a_{n}=a_{1}+(n-1)d\qquad$
(Our goal is to find $a_{1}$ and $d.)$
Use the given information (for n=16, $a_{16}=52$, and $d=5$)
$a_{16}=a_{1}+(16-1)(5)$
$ 52=a_{1}+(15)(5)\qquad$... solve for $a_{1}$
$52=a_{1}+75$
$-23=a_{1}$
So, the general rule is
$ a_{n}=-23+(n-1)(5) \qquad$... simplify
$a_{n}=-23+5n-5$
$a_{n}=5n-28$
To graph the first 6 terms, we need to plot $(n,a_{n})$ for n=1,2,...,6.
Create a table, calculating $a_{n}$ for each n, and plot the points.
