home page TI-82, TI-83 Sequences on a TI-83
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A series of activities on sequences using a TI-83
Written to complement training materials for teachers on using graphical calculators.

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3. From position-to-term rules to nth term formulas

What is the nth term of the sequence 2, 8, 18, 32...?



Any position-to-term rule can be expressed using algebra. For example, the sequences using in Section 2 produce these formulas for the nth term:

Sequence Key presses nth term
1, 3, 5 ,7, … L1 times 2 subtract 1 store L2 enter 2n-1
7, 9, 11, 13… L1 times 2 add 5 store L2 enter 2n+5
multiples of 7 L1 times 7 store L2 enter 7n
square numbers L1 times L1 store L2 enter n2
cube numbers L1 times L1 times L1store L2 enter n3
10, 9, 8, 7… 11 subtractL1 store L2 enter 11-n
     


Now we're going to develop sequence work based on the square numbers. First list L1 must contain 1, 2, 3, 4... Next a method of entering each sequence below into list L2 must be found. The position-to-term rule must be expressed as a sequence of key presses and as an algebraic formula:

Sequence Key presses nth term
1, 4, 9, 16… L1 square store L2 enter n2
9, 16, 25, 36… left bracketL1 add2right bracket square store L2 enter (n+2)2
2, 5, 10, 17… L1 square add 1 store L2 enter n2+1
2, 8, 18, 32… L1 square times 2 store L2 enter 2n2
     

What about the triangle numbers 1, 3, 6, 10... ?