Chapter 6: Sequence Application
127
Determining the General Term of a Recursion Expression
You can use the rSolve function to convert the sequence expressed by a recursion expression to the general
term format
a
n
=
f
(
n
).
0602
To determine the general term of the recursion expression
a
n
+1
=
a
n
+ 2,
a
1
= 1
About rSolve
The rSolve function returns the explicit formula of a sequence that is defined in relation to one or two previous
terms, or a system of recursive formulas.
Syntax: rSolve (Eq, initial condition-1[, initial condition-2] [ ) ]
rSolve ({Eq-1, Eq-2}, {initial condition-1, initial condition-2} [ ) ] (Eq: Equation)
Example:
To obtain the
n
-th term of a recursion formula
a
n
+1
= 3
a
n
– 1 with the
initial conditions
a
1
= 1
Calculating the Sum of a Sequence
Perform the following steps when you want to determine the sum of a specific range of the sequence of a
recursion expression or a general term expression.
0603
To calculate the sum of the general term expression
a
n
E
=
n
2
+ 2
n
– 1 in the range of
2
s
n
s
10
6-2
Graphing a Recursion
ClassPad lets you graph the values in a number table you create, and draw a cobweb diagram from the
recursion expression.
0604
To input the expression
a
n
+1
= 2
a
n
+ 1,
a
1
= 1, create a number table, and graph the values in the table
0605
To input the expression
a
n
+1
=
− 1,
a
1
= 0.5 and draw a cobweb diagram
About LinkTrace
While the Table and Graph windows are on the
display, you can activate LinkTrace. To do this,
tap in the Table window to make it active. Next,
tap
a
and then [Link]. While LinkTrace is
active, the pointer on the Graph window jumps
automatically to the point indicated by the
coordinates in the currently selected table cell.
Note that LinkTrace does not work when the
selected cell is in the first column (column
n
).
