Education Technology

Solution 10432: Generating a Recursive Sequence on the TI-83 Family, TI-84 Plus Family, TI-Nspire™ Handheld in TI-84 Plus Mode or TI-86.

How can I generate a recursive sequence on the TI-83 family, TI-84 Plus family, TI-Nspire Handheld in TI-84 Plus Mode or TI-86?

A recursive sequence is a sequence where each term is defined by its relation with the previous one, except for the first term. The TI-83 family, TI-84 Plus family, TI-Nspire Handheld in TI-84 Plus Mode, and TI-86 calculators do not have the capability to graph recursive sequences.

However there is a way to find the different elements of the sequence, write them down, and later put them into a list and to generate a graph. Please refer to the example below:

Example: Generate the sequence defined by a(n)=a(n-1)+2 and for which the first element a(1)=5.

• On the Home screen, enter {1, 5} and press [ENTER]. This defines the first element of the sequence as 5.
• Enter {Ans(1)+1, Ans(2)+2} and press [ENTER]. The calculator will display {2, 7}.

• Press [ENTER] again to display {3, 9}.
• Continue to press [ENTER] until the first element in the list represents the number of elements in the sequence being generated.

Please see the TI-83 family, TI-84 Plus family and TI-86 guidebooks for additional information.

NOTE: TI-Nspire users may refer to the TI-84 Plus family guidebook.