Question

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

Answer 1

`y = 2 - 1/3x`

Explanation:

replace `a_n` with `y` and `n` with `x`.
this gives you the equation `y = 2 - 1/3x`.

since this equation can be arranged into `y = mx+c` form
(`y = -1/3x + 2`), the graph given by the equation is a straight line.

the first three terms of the arithmetic sequence `a_n = -1/3n + 2` are `5/3, 4/3 and 1`, where `n` are `1,2 and 3`.

you should find that on the graph `y = 2 - 1/3x`, the numbers `1, and 3` for `x` match up with `5/3, 4/3 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:
`(1, 1.667) or (1, 5/3)`
`(2, 1.333), or (2, 4/3)`
`(3,1)`.