home page TI-82, TI-83 Sequences on a TI-83
© MathsNet 2001

A series of activities on sequences using a TI-83
Written to complement training materials for teachers on using graphical calculators.

 back contents more
2. Finding position-to-term rules and the 100th term

What is the 100th term of the sequence 3, 5, 7, 9...?



You can find the 10th term by pressing enter 9 times, or even the 100th term, but this is becoming an unwieldy and inefficient method.
So introduce the calculator's store button and STAT LIST display. Show how to enter the sequence 1, 2, 3…10 into list L1. The sequence 2, 4, 6… 20 can then be entered in a second list, L2, by an instruction like:
L1 * 2 store L2
Sequence Key presses
1, 3, 5 ,7, … L1 times 2 subtract 1 store L2 enter
7, 9, 11, 13… L1 times 2 add 5 store L2 enter
multiples of 7 L1 times 7 store L2 enter
square numbers L1 times L1 store L2 enter
cube numbers L1 times L1 times L1store L2 enter
10, 9, 8, 7… 11 subtractL1 store L2 enter
   

Typical screen displays:
screen 5 screen 6

The Key presses listed above are in fact "position-to-term" rules and these are very useful in finding any term in a sequence, for example the 100th term.
Set up your calculator so that the L1 contains the numbers 1, 2, 3, 4, 100 and then work on identifying what the sequences are and in particular the 100th term:
Position-to-term rules Sequence 100th term
L1 times 3 store L2 enter 3, 6, 9, 12... 300
L1 times 5 store L2 enter 5, 10, 15, 20... 500
L1 add 3 store L2 enter 4, 5, 6, 7... 103
L1 times 2 add 1 store L2 enter 3, 5, 7, 9... 201
     

screen 7 screen 8