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Focus A: Building on the Past

Suppose we want to graph the first 10 terms of the sequence given by the explicit  formula . Firstly, you must realize that the ordered pairs to be plotted are determined by . Since we are to graph the first 10 terms, there will be 10 ordered pairs, each of which is determined by substituting the values 1 through 10 into the explicit formula. You can instruct the calculator to do this by following the steps below.

  1. Press MODE. Presently the calculator is set to graph equations written in function form and you need to graph a sequence. To make this change, scroll down to line 4 and select Seq. Press ENTER.
  2. Press Y=
  3. Set nMin = 1 and  = 20 + 2.5n. Now that you are using the sequence graphing function, pressing the X,T,,n will result in the variable n as opposed to the usual x.
  4. Press WINDOW. Set nMin = 1, nMax = 10, PlotStart = 1, PlotStep =1, Xmin = 0, Xmax = 10, Xscl = 1, Ymin = 20, Ymax = 50, Yscl = 5. In this step, you are telling the calculator what values you want for the x-coordinate of each point (i.e. the values of n), and the increments by which it is to increase. In this case you are choosing the numbers 1 through 10 for n. When you select the values for Ymin and Ymax, you must remember  they represent each value of 20 + 2.5n as n goes from 1 to 10. The smallest value is 22.5 which occurs when n is 1. The largest value is 45 which occurs when n is 10. Hence, the Ymin was chosen to be 20 and the Ymax was set at 50, going up by a scale of 5.
  5. Press GRAPH.
  6. The TRACE function can be used to read off points. 

If you would a visual demonstration showing you how to graph a sequence on the TI-83 Plus, click here.

If you wanted to graph 100 terms, you would follow the same procedure but it would be necessary to change the values of nMax, PlotStep, Xmax, Xscl, Ymax and Yscl appropriately. 

  •   nMax would now be 100 since there are 100 terms. 
  • It wouldn't be wise to go from 1 to 100 by increments of 1, so the PlotStep should be changed to say 5.
  •   Xmax should now be 100 as well, and the Xscl set to 5. 
  • The value of Ymax would be about 300 since when n = 100, the sequence has a value of 270.
  •  You can change the Yscl to 25, as this is a reasonable increment by which to go from 20 to 300.