The program Sequen86 plots one recursive sequence with one initial condition. The function is stored in variable y1, with x presenting y1(n-1). The initial condition is assumed to be y1(1).

This program was originally posted on ticalc.org on April 28, 2001. Link: https://www.ticalc.org/archives/files/fileinfo/186/18667.html

18 years, wow, how time flies.

**TI-86 Program Sequen86**

(354 bytes)

Func

FnOff

PlOff

ClLCD

DelVar(L1)

DelVar(L2)

Outpt(6,1,”Let y1 = u”)

Outpt(7,1,”Let x = n-1”)

InpSt “y1 =”, Y

St>Eq(Y,y1)

Input “Initial Cond: “,I

Input “# of Steps: “,S

{I} → U

For(N, dimL U+1, S+1, 1)

y1(U(N-1)) → U(N)

End

seq(x,x,1,S+1) → L1

U → L2

0 → xMin

S+1 → xMax

min(U) – 1 → yMin

max(U) + 1 → yMax

Plot1(1,L1,L2)

FnOff 1

Disp “L1 = n”

Pause “L2 = u”

DispG

Example:

u(n) = u(n-1)/3 + 1/4

Initial condition, u(1) = 1/5

Number of Steps: 10

Set up for Sequen86:

y1 = x/3 + 1/4

**The 2019 Version**

Here is an alternate version, SEQGRAPH. Use U for U(n-1) and N for n. The program allows the initial condition for any value of N.

**TI-86 Program SEQGRAPH**

(277 bytes)

InpSt “U1(U,N) = “,S1

St>Eq(S1,U1)

Input “N Start = “,N

Input “U0 = “,U

Input “Steps: “,S

S + 1 → dimL xList

S + 1 → dimL yList

N → xList(1)

U → yList(1)

For(I, 2, S+1)

xList(I-1) + 1 → N

N → xList(I)

yList(I-1) → U

U1 → yList(I)

End

FnOff

PlOff

PlOn 1

Plot1(1,xList,yList)

ZData

Example:

u(n) = u(n-1)/3 + 1/4

Initial condition, u(1) = 1/5

Number of Steps: 10

Set up for SEQGRAPH:

U1 = U/3 + 1/4

N Start: 1

U0 = 1/5 (initial condition)

Eddie

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