Series Program finds sum when input first No. last No. & diff.

Arithmetic Series

Introduction: An arithmetic sequence is an ordered list of numbers when the difference of any two successive numbers is constant. An arithmetic series is the sum of an arithmetic sequence. A geometric sequence is a sequence such that each successive term is obtained from the previous term by multiplying by a fixed number called a common ratio. The sequence 5, 10, 20, 40, 80, .... is an example of a geometric sequence. The pattern is that we are always multiplying by a fixed number of 2 to the previous term to get to the next term. Program written by [Erick Hunziker (MTLTV1765@aol.com)], modified by [RRoberts (http://freetutorials.name)].

Note: This program is in TI-BASIC and can be entered into the calculator by the calculator keyboard. Do not enter the outline, line numbers or comments, they are for reference only. The example programs below are for testing the program. If you get the values listed, the program was entered correctly. If not, check the listing and correct it. The program has been checked and tested.


Arithmetic Sum	Arithmetic Term	Geometric Sum	Geometric Term

Description: This program will find the arithmetic and/or Geometric sum of a sequence. It will also calculate an individual term (or the nth term).

TI-83 Calculator Emulator

A step by step process for downloading a TI Emulator. An emulator is basicly the computer version of a TI 83 Calculator. It works like the calculator but from your computer screen.

Place the "ROM" in the same folder as the TI emulator for it to work.

Outline:
	Line 1.	Clear Screen
	Line 3 - 7.	Prep (strings)
	Line 8.	Menu	Menu (Arith/Geo)
	Line 10.	Lbl A Arithmetic Sequence
	Line 11 - 13.	Input (Arithmetic Sequence)
	Line 14 - 16.	Formula (Arithmetic Sum)
	Line 18.	Arithmetic Sum
	Line 22.	Arithmetic (nth) Term
	Line 23 - 25.	Input (Arithmetic (nth) Term)
	Line 26.	Formula (Arithmetic Term)
	Line 28.	nth Term
	Line 32.	Lbl G Geometric Sequence
	Line 33.	Menu	Menu (Finite/Infinite)
	Line 34.	Finite Sequence
	Line 35 - 37.	Input (Finite Sequence)
	Line 38.	Formula (Finite Sum)
	Line 40.	Geometric Sum
	Line 43.	Infinite Sequence
	Line 45 - 46.	Input (Infinite Sequence)
	Line 49.	Formula (Infinite Sum)
	Line 51.	Infinite Series Sum
		Examples
		Series Formulas
		Reference Commands
		Reference Links

prgmSERIES

Line	Command or Statement	Comments
1.	ClrHome	Clear Screen
2.	Float
3.	"FIRST TERM = ->Str1	FIRST TERM
4.	"LAST TERM = ->Str2	LAST TERM
5.	"COMMON DIFFER = ->Str3	COMMON DIFFER
6.	"SUM OF SERIES = ->Str4	SUM OF SERIES
7.	"COMMON RATIO = ->Str5	COMMON RATIO
.	"NTH TERM = ->Str6	NTH TERM
8.	Lbl 1	Menu - Type
9.	Menu("SELECT TYPE", "ARITHMETIC",A,"NTH TERM",T,"GEOMETRIC",G,"QUIT",Q)
10.	Lbl A	Arithmetic Sequence
11.	Input Str1,F	First Term
12.	Input Str2,L	Last Term
13.	Input Str3,D	Common Difference
14.	L-(F-D)->A	Formula (Arithmetic Sum)
15.	A/D->B
16.	(B(F+L))/2->S
17.	ClrHome	Clear Screen
18.	Disp Str4	Sum of Arithmetic Series
19.	Pause S
20.	ClrHome	Clear Screen
21.	Goto 1	Menu - Type
22.	Lbl T	nth Term
23.	Input Str1,F	First Term
24.	Input Str3,D	Common Difference
25.	Input Str6,N	nth Term
26.	A1+(N-1)D->AN	Formula (Arithmetic Term)
27.	ClrHome	Clear Screen
28.	Disp Str6	Arithmetic Term
29.	Pause S
30.	ClrHome	Clear Screen
31.	Goto 1	Menu - Type
32.	Lbl G	Geometric Sequence
33.	Menu("SELECT TYPE","FINITE",F,"INFINITE",I)
34.	Lbl F	Finite Sequence
35.	Input Str1,F	First Term
36.	Input Str2,L	Last Term
37.	Input Str5,R	Common Ratio
38.	(F-(L*R))/(1-R)->S	Formula (Finite Sum)
39.	ClrHome	Clear Screen
40.	Disp Str4	Sum of Geometric Series
41.	Pause S
42.	Goto 1	Menu - Type
43.	Lbl I	Infinite
44.	ClrHome	Clear Screen
45.	Input Str1,F	First Term
46.	Input str5,R	Common Ratio
47.	If abs(R)<1
48.	Then
49.	F/(1-R)->S	Formula
50.	ClrHome	Clear Screen
51.	Disp Str4	Sum of Infinite Series
52.	Pause S
53.	Goto 1
54.	Else
55.	ClrHome	Clear Screen
56.	Disp Str4	Sum of Series
57.	Disp "Not Valid"	Not Valid
58.	Pause
59.	Goto 1
60.	End
61.	Lbl Q	Quit
62.	ClrHome	Clear Screen
63.	Stop	Stop

Examples:

	Arithmetic Sequence	Geometric Sequence
	F = First Term	F = First Term
	L = Last Term	L = Last Term
	D = Common Difference	R = Common Ratio
	S = Arithmetic Sum	S = Geometric Sum
	S = ((L - (F - D)/ D)(F + L ))/2	S = (F - (L*R))/(1- R)
	Find the sum of the sequence:	Find the sum of the sequence:
	1 + 2 + 3 ...985	5 + 10 + 20 ...640
	Answer: 485605	Answer: 1275
	S = ((985 - (1 - 1)/ 1)(1 + 985))/2 = 485605	S = (5 - (640 * 2))/(1 - 2) = 1275

Reference:

Formulas:

To find the sum of a certain number of
terms of an arithmetic sequence:
calculator

where Sn is the sum of n terms (nth partial sum),
a1; is the first term,
an; is the nth term.

To find any term
of an arithmetic sequence:

where a1 is the first term of the sequence,
d is the common difference,
n is the number of the term to find.

Reference:
Commands or Statements:: Catalog Press [2nd] CATALOG to display the CATALOG. Press /\ or \/ to scroll the CATALOG until the selection cursor points to the item you want. To jump to the first item beginning with a particular letter, press that letter; (alpha-lock is on). Items that begin with a number are in alphabetical order according to the first letter after the number. For example, 2.PropZTest( is among the items that begin with the letter P). Functions that appear as symbols, follow the last item that begins with Z. Press [ENTER] to paste the item to the current screen.; ClrHome ClrHome (clear home screen) clears the home screen during program execution.; Disp displays text or value specified; Fix sets fixed-decimal mode for number of decimal places; Float sets floating decimal mode. Displays decimal with no trailing zeros; Goto goes to label specified. Goto requires a line label be implemented as a destination; If; Then; Else Executes commands from Then to Else If condition true: or from Else to End if condition false; Input prompts for value to store to variable. Requires user input through keypad.; Lbl creates a label of one or two characters. Lbl (label) and Goto (go to) are used together for branching. Lbl specifies the label for a command. label can be one or two characters (A through Z, 0 through 99, or thea). Goto causes the program to branch to label when Goto is encountered.; Menu generates a menu of up to seven items. The menu title is enclosed in quotation marks ( " ). Up to seven pairs of menu items follow. Each pair comprises a text item (also enclosed in quotation marks) to be displayed as a menu selection, and a label item to which to branch if you select the corresponding menu selection.; output( row, column) displays text or value beginning at specified row and column. Output( displays text or value on the current home screen beginning at row (1 through 8) and column (1 through 16), overwriting any existing characters.; Pause [value] Displays value; suspends program execution until you press [ENTER]. Pause with value displays value on the current home screen. Value can be scrolled.; Str# (# is number) A string is a sequence of characters that you enclose within quotation marks. To enter a string on a blank line on the home screen or in a program, follow these steps.
1. Press . ["] to indicate the beginning of the string.
2. Enter the characters that comprise the string. Use any combination of numbers, letters, function names, or instruction names to create the string. To enter several alpha characters in a row, press [2nd] [A.LOCK] to activate alpha-lock.
3. Press . ["] to indicate the end of the string.

Series Program with Formulas

Arithmetic Series

prgmSERIES