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

1 Answer
Jun 17, 2018

Answer:

#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)#.