# How do you graph the arithmetic sequence a_n=2-1/3n?

Jun 17, 2018

$y = 2 - \frac{1}{3} x$

#### Explanation:

replace ${a}_{n}$ with $y$ and $n$ with $x$.
this gives you the equation $y = 2 - \frac{1}{3} x$.

since this equation can be arranged into $y = m x + c$ form
($y = - \frac{1}{3} x + 2$), the graph given by the equation is a straight line.

the first three terms of the arithmetic sequence ${a}_{n} = - \frac{1}{3} n + 2$ are $\frac{5}{3} , \frac{4}{3} \mathmr{and} 1$, where $n$ are $1 , 2 \mathmr{and} 3$.

you should find that on the graph $y = 2 - \frac{1}{3} x$, the numbers $1 , \mathmr{and} 3$ for $x$ match up with $\frac{5}{3} , \frac{4}{3} \mathmr{and} 1$ for $y$.

here is the graph:

graph{2 - 1/3x [-6.25, 13.75, -5.16, 4.84]}

scrolling along it gives you:
$\left(1 , 1.667\right) \mathmr{and} \left(1 , \frac{5}{3}\right)$
$\left(2 , 1.333\right) , \mathmr{and} \left(2 , \frac{4}{3}\right)$
$\left(3 , 1\right)$.