- WELCOME TO A VIDEO ON SEQUENCES
ON THE TI-83 OR 84 GRAPHING CALCULATOR.
THIS VIDEO WILL SHOW HOW TO GENERATE AND GRAPH A SEQUENCE
ON THE GRAPHING CALCULATOR.
SO, FOR EXAMPLE, IF WE HAVE A SEQUENCE
GENERATED BY "A" SUB N = 1 + 1/N,
WE CAN GENERATE THIS ON THE GRAPHING CALCULATOR.
THE FIRST THING WE SHOULD DO
IS PUT OUR GRAPHING CALCULATOR IN SEQUENCE MODE.
IF WE PRESS THE MODE KEY,
YOU LOOK AT THE FOURTH ROW THIS LAST OPTION, SEQ,
IS FOR SEQUENCE MODE.
LET'S GO AHEAD AND DO THAT.
SO WE JUST MOVE THE CURSOR DOWN THERE
AND HIGHLIGHT SEQUENCE.
PRESS ENTER AND THEN WE CAN GO AHEAD
AND GO BACK TO THE HOME SCREEN.
LET'S SHOW HOW WE CAN GENERATE THE FIRST 10 TERMS
OF THE SEQUENCE FROM THE HOME SCREEN.
IF WE PRESS 2nd, STAT, WHICH BRINGS UP THE LIST MENU
AND THEN RIGHT ARROW ONCE TO OPS, OPTION 5 IS FOR SEQUENCE.
SO WE CAN JUST PRESS 5,
AND THIS COMES BACK TO THE HOME SCREEN.
NEXT, WE'RE GOING TO TYPE IN THE FORMULA 1 + 1/N.
NOW, WHEN WE PRESS THE VARIABLE, WHICH IS NORMALLY X,
IT WILL NOW BE N,
BECAUSE WE'RE IN SEQUENCE MODE.
COMMA, AND THEN WE'LL PRESS N AGAIN FOR THE VARIABLE
USED FOR THE FORMULA.
COMMA, WE WANT N TO START AT 1, COMMA, AND END AT 10.
CLOSE PARENTHESIS, AND WHEN WE PRESS ENTER,
THE CALCULATOR IS SHOWING THE TERMS IN THE SEQUENCE.
NOTICE THERE'S MORE TERMS ON THE RIGHT,
SO WE'D HAVE TO PRESS THE RIGHT ARROW TO SEE MORE TERMS.
NOW, ONE THING WE NOTICE RIGHT AWAY
IS THAT THESE ARE EXPRESSED IN DECIMAL FORM.
IF WE WANT THE TERM TO BE EXPRESSED IN FRACTION FORM,
WE CAN PRESS MATH, ENTER, ENTER,
AND THEN THE TERMS WILL BE IN FRACTION FORM.
THE SECOND WAY TO SHOW THIS SEQUENCE WOULD BE TO GRAPH IT.
SO LET'S GO AHEAD AND SHOW
HOW YOU CAN GRAPH THE SEQUENCE AS WELL.
IF WE PRESS Y =, IN U OF N
WE'RE GOING TO TYPE IN THE FORMULA 1 + 1/N.
WE CAN SEE THAT N IS GOING TO START AT 1,
SO LET'S GO AHEAD AND PRESS GRAPH.
NOTICE FROM THIS WINDOW WE'RE NOT GETTING A GOOD PICTURE
OF THE SEQUENCE.
SO LET'S GO AHEAD AND PRESS WINDOW.
NOTICE N IS GOING TO GO FROM 1 TO 10.
IT'S GOING TO START AT 1 AND GO BY 1.
THAT'S GOOD, BUT NOTICE THE X AXIS GOES FROM -15 TO +15.
LET'S CHANGE THIS FROM -2 TO, LET'S SAY, 11.
AND THEN FOR THE Y MINIMUM/Y MAXIMUM,
WE KNOW THAT THE VALUES IN THE SEQUENCE AREN'T VERY LARGE.
LET'S GO AHEAD AND HAVE THE Y MINIMUM OF -1
AND THE Y MAXIMUM AT 2.
SEE WE HAVE TO PLAY AROUND WITH THESE VALUES
TO GET A NICE GRAPH OF THE SEQUENCE.
NOW IF WE PRESS GRAPH,
NOTICE WE HAVE A MUCH BETTER GRAPH OF THE SEQUENCE,
AND IF WE PRESS TRACE FROM HERE,
IT'LL SHOW US THE COORDINATES OF EACH POINT.
REMEMBER THAT THE X COORDINATE WOULD BE N,
AND THE Y COORDINATE WOULD BE THE TERM IN THE SEQUENCE.
SO WHEN N = 1, THE SEQUENCE WOULD GENERATE THE TERM 2.
AND WE CAN SEE HERE IF WE LET N = 1, WE'D HAVE 1 + 1 = 2.
NOW, IF WE PRESS THE RIGHT ARROW,
WE CAN VIEW EACH TERM IN THE SEQUENCE.
NOW, IT WILL BE EXPRESSED IN DECIMAL FORM HERE,
AND THERE'S NOT MUCH WE CAN DO ABOUT IT FROM THIS VIEW.
SO WE CAN SEE THAT IT LOOKS LIKE THE TERMS ARE APPROACHING
THE VALUE OF 1.
LET'S GO AHEAD AND TAKE A LOOK AT ANOTHER ONE.
HERE WE HAVE 1 + 1/2N.
LET'S GO BACK TO THE HOME SCREEN.
LET'S CLEAR THIS AND REVIEW IT ONE MORE TIME.
WE'RE GOING TO PRESS 2nd, LIST, RIGHT ARROW ONCE TO OPS,
PRESS OPTION 5 FOR SEQUENCE, TYPE IN THE FORMULA.
SO WE HAVE 1 + 1/2N, COMMA N, COMMA 1, COMMA,
HOWEVER MANY TERMS WE WANT.
LET'S GO AHEAD AND GENERATE THE FIRST 10 TERMS AGAIN.
CLOSE PARENTHESIS, PRESS ENTER,
AND THERE ARE THE TERMS.
IF WE PUSH THE RIGHT ARROW, WE CAN SEE MORE AND MORE TERMS.
NOTICE HOW EACH TERM INCREASES BY 1/2,
AND THEN IT STOPS AT 6, BECAUSE WHEN N IS 10,
WE HAVE 1 + 1/2 x 10 OR 1 + 5 WOULD GIVE US 6.
AND, AGAIN, TO GRAPH THIS SEQUENCE,
WE JUST NEED TO CHANGE THE FORMULA HERE TO 1 + 1/2N,
AND THEN PRESS GRAPH.
AND NOTICE AGAIN, WE SHOULD ADJUST OUR WINDOW.
WE JUST SAW THE LAST TERM IN THE SEQUENCE,
IF WE HAVE 10 TERMS, WAS 6.
SO WE NEED TO INCREASE OUR Y MAXIMUM TO AT LEAST 6.
LET'S MAKE IT 8.
HERE WE CAN SEE THAT THE VALUE OF EACH TERM
INCREASES WITHOUT BOUND.
OKAY, THAT'S GOING TO DO IT
FOR USING THE GRAPHING CALCULATOR FOR SEQUENCES.
I HOPE YOU HAVE FOUND THIS VIDEO HELPFUL.
THANK YOU FOR WATCHING.