The Sequence Aplet - HP 39gs Master Manual

T S
T S
H E E Q U E N C
H E E Q U E N C
This aplet is used to deal with sequences, and indirectly series, in both non-recursive form (where T
function of n) and implicit/recursive/iterative form (where T
Recursive or non-recursive
Examples of these types of sequences are:
(explicit/non-recursive)
T = 3n − 1 .....
n
T = n
2
.....
n
T = 2
n
.....
n
(implicit/recursive)
T = 2T − 1 ;T
n n−1
T = − T
5
n n−1
T = T + T ;T
n n−1 n−2
As with most aplets, the Sequence aplet starts in the
you enter formulas. The Sequence aplet uses the terminology U(N)
rather than the other commonly used T
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 – ie. for
N = 1,2,3,4...
First, second & general terms
Each definition has three entries -
(see above) but it is not always necessary to
U1(N)
supply all three.
For example, if the sequence is non-recursive then only the
needs to be filled in, with the other two entries calculated automatically
from the definition as shown in the sequence of two screens shown right.
A
A
E P L E T
E P L E T
{ }
2, 5,8,11,14,.....
{ }
1, 4, 9,16, 25,.....
{ }
2, 4,8,16, 32,.....
= 2
.....
1
= 2
;T .....
1
= 1,T = 1
.....
1 2
for its definitions in order to
n
and
U1(1), U1(2)
is a function of T
n
{ }
2, 3, 5, 9,17,.....
{ }
2, 3, 2, 3, 2,.....
{ }
1,1, 2, 3, 5,8.....
view when
SYMB
entry
U1(N)
99
is a
n
).
n-1
14