107
T
T
H
H
E
E
S
S
E
E
Q
Q
U
U
E
E
N
N
C
C
E
E
A
A
P
P
L
L
E
E
T
T
This aplet is used to deal with sequences, and indirectly series, in both non-
recursive form (where T
n
is a function of n) and implicit/recursive/iterative
form (where T
n
is a function of T
n-1
).
Recursive or non-recursive
Examples of these types of sequences are:
(explicit/non-recursive)
{
}
{
}
{
}
2
3
1 .....
2,5,8,11,14,.....
.....
1, 4,9,16, 25,.....
2
.....
2, 4,8,16,32,.....
n
n
n
n
T
n
T
n
T
=
−
=
=
(implicit/recursive)
{
}
{
}
{
}
1
1
1
1
1
2
1
2
2
1 ;
2
.....
2,3,5,9,17,.....
5
;
2
.....
2,3, 2,3, 2,.....
;
1,
1
.....
1,1, 2,3,5,8.....
n
n
n
n
n
n
n
T
T
T
T
T
T
T
T
T
T
T
−
−
−
−
=
−
=
= −
=
=
+
=
=
As with most aplets, the Sequence aplet starts
in the
SYMB
view when you enter formulas.
The Sequence aplet uses the terminology U(N)
rather than the other commonly used T
n
for its
definitions in order to avoid having to use
subscripts which would not show up well on
the screen. All functions of this type are assumed to be defined for the
positive integers only - for
N = 1,2,3,4…
First, second & general terms
Each definition has three entries -
U1(1), U1(2)
and
U1(N)
(see above).
If the sequence is non-recursive then only the
U1(N)
entry need be filled in,
with the other two entries calculated
automatically from the definition.
Let’s start with a non-recursive
sequence of
2
n
n
T
=
. If you type it in
as shown right (using the
XT
θ
button to get N), press
ENTER
and then watch carefully, you will see the entries
for
U1(1)
and
U1(2)
filled in automatically.
