Using a TI-83/84 for Sequences and Series
Lily Yen
December 1, 2016
Sequences
First tell your calculator that you are working with sequences: MODE
then select Seq from the “Func Par Pol Seq” set of choices and select Dot
from the “Connected Dot” set one line further down. Press QUIT to Press
to get
return to the main screen.
2nd
MODE
QUIT
A explicitly given sequence
To plot first few terms of the sequence { n+2
}∞ , press Y = . Then set
n−1 n=2
nMin to 2, u(n) to (n + 2)/(n − 1), and clear the u(nMin) entry. (If you Press
fail to clear u(nMin), the first few points of your graph may be wrong.) get n
You can now plot the sequence by pressing GRAPH . You can adjust the
plotting window though WINDOW and ZOOM as usual. For example,
under WINDOW ,
nMin
nMax
PlotStart
PlotStep
Xmin
Xmax
Xscl
Ymin
Ymax
Yscl
=
=
=
=
=
=
=
=
=
=
X,T,θ,n
to
2 Your sequence begins with a2
20 Your sequence ends with a20
1 Your plot begins with the first term, a2
1
0
20
1
0
2
1
Xmin is set to 0 above to draw the y-axis even if the sequence is drawn
only from n = 2.
A recursively given sequence
Consider the sequence given by an = an−1 + n5 for n > 0 and a0 = 1. Press 2nd 7 to get
Again press Y = and set nMin to 0, u(n) to u(n − 1) + 5/n,and u(nMin) the function u. This
is different from
to 0. Again, you can change the WINDOW settings:
ALPHA 5 which
gives the number U
1
nMin
nMax
PlotStart
PlotStep
Xmin
Xmax
Xscl
Ymin
Ymax
Yscl
=
=
=
=
=
=
=
=
=
=
0
20
1
1
0
20
1
0
20
1
nMin
nMax
PlotStart
PlotStep
Xmin
Xmax
Xscl
Ymin
Ymax
Yscl
or
=
=
=
=
=
=
=
=
=
=
0
40
16
1
0
40
1
15
25
1
Changing nMin yields a completely different sequence! Change PlotStart
to begin the plot later in the sequence. With the left-hand settings you
get a0 , . . . , a20 . Since a15 is the 16th term of this sequence, the right-hand
settings give you a15 , . . . , a40 .
If your recursive sequence needs more than one seed value, give u(nMin)
as a list. For example, if an = an−1 + an−2 , a0 = 0, and a1 = 1, then under
Y = set nMin to 0, u(n) to u(n − 1) + u(n − 2), and u(nMin) to {0, 1}. Press
{
Series
Note that is u(n) = nk=1 ak , then u(n) = u(n − 1) + an , so you can plot
partial sums in the same manner as recursively given sequences above.
P
2k
For example, to plot the partial sums of ∞
k=0 k! , press Y = and set
nMin to 0, u(n) to u(n − 1) + 2n /n!, and u(nMin) to 20 /0!. Then use
WINDOW settings like
P
nMin
nMax
PlotStart
PlotStep
Xmin
Xmax
Xscl
Ymin
Ymax
Yscl
=
=
=
=
=
=
=
=
=
=
0
10
1
1
0
10
1
0
10
1
to see the partial sums level off towards e2 ≈ 7.39.
2
2nd
(
to get