A miniature Sequence-cracking device that gives any requested term, a term-to-term rule, and vene a formula for the sequence! Made in DbPro, but will work in DBC too.

What does it do?
----------------
-> Allows you to obtain any term from a sequence
-> Shows the formula for a sequence (to work out any term)

Huh?
------
Ok, you don't really understand. Here's an example sequence:

9 , 18 , 27 , 36

Its quite obvious what the rule is here [+9 each time]. Yet, there
is a problem:

********************************************************
What do I do if I want the 687th number in the sequence?
********************************************************

That's where this program comes in handy, and not only does
it do this, it also gives you a formula to work out any term!


KNOWN LIMITATION
-----------------
The program cannot currently do descending sequence
[E.g: -1 , -2 , -3] as it cannot work out the FiTermHook.
The program shall generate an error if this happens:

"Term to term rule is UNstable (NON Linear)..."


I'm currently fixing this issue

(So don't do descending sequences unless you want wrong answers!)

                                    ` This code was downloaded from The Game Creators
                                    ` It is reproduced here with full permission
                                    ` http://www.thegamecreators.com
                                    
                                    remstart
******************************************************
A9x8 Sequence cracking device
******************************************************

1/7/2003

What does it do?
----------------
-> Allows you to obtain any term from a sequence
-> Shows the formula for a sequence (to work out any term)

Huh?
------
Ok, you don't really understand. Here's an example sequence:

               9 , 18 , 27 , 36

Its quite obvious what the rule is here [+9 each time]. Yet, there
is a problem:

********************************************************
What do I do if I want the 687th number in the sequence?
********************************************************

That's where this program comes in handy, and not only does
it do this, it also gives you a formula to work out any term!


KNOWN LIMITATION
-----------------
The program cannot currently do descending sequence
[E.g:  -1 , -2 , -3] as it cannot work out the FiTermHook.
The program shall generate an error if this happens:

    "Term to term rule is UNstable (NON Linear)..."


I'm currently fixing this issue

(So don't do descending sequences unless you want wrong answers!)


----------------------------------------------------------------
remend






dim calc1(1)
dim calc2(1)
dim formula$(1)
set text font "verdana"
set text to bold
set text size 18
ink RGB(255,0,0),1

print "THIS PROGRAM ONLY WORKS WITH LINEAR SET-PATH SEQUENCES"
PRINT "PLEASE DOUBLE-CHECK THE RESULTS OF THIS PROGRAM BEFORE"
PRINT "USING IN IMPORTANT PROJECTS OR WORK"
PRINT " "
print "THE USAGE OF EXTREMELY LARGE NUMBERS IN THIS PROGRAM CAUSES"
PRINT "SPARODIC NEGATIVE OUTPUT - YOU HAVE BEEN WARNED"
PRINT

PRINT "PRESS ANY KEY"
SUSPEND FOR KEY
CLS
set text to normal
ink RGB(255,255,255),1
print "Enter sequence details"
print "[You'll need the first THREE terms of the sequence]"
print " "
input "First term? ";a
input "Second term? ";b
input "Third term? ";c
cls
calculate(a,b,c)
print " "
cls
print "Sequence formula: ";formula$(1)
print "Enter any term number to retrieve the equivalent from the sequence"
do
print " "
input "Term> ";term

Termnew=term*calc1(1)
Newnum=termnew+calc2(1)
print "Answer: ";newnum
print " "
loop




function calculate(first,second,third)
firstnum=first
secondnum=second
thirdnum=third
print "Please wait......"
print "Function Copyright David Roberts 1999-2005(C)"
print "Uses similar systems to XforV() copyright Mathe-Deutschland 2004(C)"
print "Working Difa01..."
if second>first
print "Secterm>FiTerm"
difa01=first-second
else
print "Assuming FiTerm>Secterm...."
difa01=second-first
endif
print "Difa01 = ";difa01


print "Working PrimaryDifb01...."
print "WARNING: MAY GENERATE UNSTABLE CONSQ() IF B<A!!!!"
difb01=second-first
print "Difb01 = ";difb01
print "Algerbraic Sequence cracker"
print "[Will return to window soon]"
print " "
print "Retrieving term information..."
wait 2500
print "Linear - Easy retrieval expected..."
print "Adding Mathematik hooks..."
wait 4000
print "Retrieving Term to term rule..."

if secondnum>firstnum
Calc1=secondnum-firstnum
endif
if secondnum<firstnum
Calc1=firstnum-secondnum
print "Test (T2) ___";calc1;""
endif
if thirdnum>secondnum
calcnew=thirdnum-calc1
endif
if calcnew=secondnum
print "Term to term rule is stable (Linear)...."
print "Now cracking.."
goto easy
else
ink RGB(255,0,0),1
print "Term to term rule is UNstable (NON Linear)...."
print "Now ATTEMPTING cracking.."

print
print "*****THE OUTCOME MAY BE WRONG*******"
ink RGB(255,255,255),1
endif

easy:
wait 2000
print "Term to term (Est.): ";calc1;""
print " "
print "Performing secret formula..."
wait 3000
Calc2=firstnum-calc1
calc3=calc*3
print " "
print "T[n]  = ";calc2;"+";calc1;"n"
ca$=str$(calc1)
cb$=str$(calc2)

Termnew=term*calc1(1)
Newnum=termnew+calc2(1)
formula$(1)="Term answer = ( Term * "+ca$+" ) + "+cb$

print "Please wait..."
wait 3000
calc1(1)=calc1
calc2(1)=calc2
endfunction