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Chapter 6: Advanced Graphing Features — Advanced Keyboard
4. Graphing Sequences
The sequence graph mode can store and simultaneously draw three graph equations
u(n), v(n), and w(n).
Variables u, v, and w are entered as @ u (or v, w).
Use X to enter the natural number n.
A sequence is an ordered set of numbers with a defined relation-
ship. The
recursive
sequential formulas can be described as
u
n
= u
n-1
+ d and/or
u
n
= u
n-1
× r
where u
n
is the n-th term, d is the common difference, and r is the
ratio. In many occasions however, the term before u
n-1
(i.e., one
term before u
n
) is not known. In such cases, the
explicit
formulas
must then be derived as:
u
n
= u
1
+ d × (n - 1) and/or
u
n
= u
1
× r
n-1
where u
n
is the n-th term, u
1
is the first term of the sequence, d is
the common difference, and r is the ratio.
A sequence {2, 4, 8, 16, 32, ...} may suggest the following
recursive sequence expression:
u
n
= 2 × 2
n-1
or it may also suggest the following non-recursive expression:
u
n
= 2
n
The calculator can plot sequential graphs in three different
schemes, as follows:
n
-based (Time)
The u
n
values will be plotted
against the n value.