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Chapter 6: Sequence Graphing 158
Recursive Sequences
Recursive SequencesRecursive Sequences
Recursive Sequences
In a recursive sequence, the
nth term in the sequence is defined in relation to the
previous term or the term that precedes the previous term, represented by
u(nN1) and
u(nN2). A recursive sequence may also be defined in relation to n, as in u(n)=u(nN1)+n.
For example, in the sequence below you cannot calculate u(5) without first calculating
u(1), u(2), u(3), and u(4).
Using an initial value
u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, ... .
Note: On the TI-84 Plus, you must type each character of the terms. For example, to
enter
u(nN1), press y [u] £ „ ¹ À ¤.
Recursive sequences require an initial value or values, since they reference undefined
terms.
• If each term in the sequence is defined in relation to the previous term, as in
u(nN1),
you must specify an initial value for the first term.
• If each term in the sequence is defined in relation to the term that precedes the
previous term, as in
u(nN2), you must specify initial values for the first two terms.