RD SEQUENCES OF NUMBERS ARE LISTS OF NUMBERS THAT ARE MADE 00000100 UP WITH A PATTERN; IF YOU LOOK AT THE FIRST FEW NUMBERS, 00000200 AND CAN FIGURE OUT HOW THE NUMBERS ARE RELATED TO EACH 00000300 OTHER, OR HOW EACH NUMBER IS FORMED FROM THOSE THAT GO 00000400 BEFORE IT, YOU HAVE CRACKED THE "CODE" OF THE SEQUENCE. 00000500 00000600 FOR EXAMPLE, THE SEQUENCE 2,4,6,8... IS FORMED BY ADDING 00000700 TWO TO EACH NUMBER TO GET THE FOLLOWING NUMBER, OR YOU MAY 00000800 THINK OF IT AS COUNTING BY TWO. 00000900 PRESS THE LEFT ARROW KEY WHEN YOU ARE READY TO CONTINUE. 00001000 QU DO YOU KNOW WHAT A SEQUENCE IS. 00001100 CA NO 00001200 CB I DO NOT 00001300 TY IN A SEQUENCE THERE IS A RULE FOR FORMING EACH NEW 00001400 NUMBER FROM THE PRECEDING NUMBERS, AND YOU HAVE TO FIND 00001500 THE RULE. FOR EXAMPLE IN THIS SEQUENCE 1, 2, 4, 8, 16, ... 00001600 EACH NUMBER IS OBTAINED FROM THE PRECEDING NUMBER BY 00001700 DOUBLING IT. SOMETIMES THE RULE FOR FORMING THE SEQUENCE 00001800 MAY BE STATED IN VARIOUS WAYS--THE EXAMPLE HERE MAY BE 00001900 THOUGHT OF AS POWERS OF 2. 00002000 CA YES 00002100 CB OF COURSE 00002200 BR PROB3 0000000T00002300 UN PLEASE TYPE YES OR NO 00002400 LA BACK 00002500 QU THE RULE FOR FORMING THE SEQUENCE 1, 2, 3, 4, 5,... 00002600 IS ADD ONE. WRITE A SEQUENCE STARTING WITH ONE IN 00002700 WHICH YOU DOUBLE EACH NUMBER AND ADD ONE TO GET THE 00002800 NEXT NUMBER. WRITE THE FIRST THREE TERMS, SEPARATING 00002900 TERMS WITH COMMAS. 00003000 CA 1, 3, 7 00003100 CB 1,3,7 00003200 CB 1,3,7, 00003300 CB 1, 3, 7, 00003400 CB ONE, THREE, SEVEN, 00003500 CB ONE, THREE, SEVEN 00003600 TY VERY GOOD. THE FIRST THREE NUMBERS ARE 1,3,7, AND IF 00003700 SEVERAL MORE NUMBERS WERE GIVEN THE SEQUENCE WOULD LOOK 00003800 LIKE THIS 1, 3, 7, 15, 31, 63, 127, ... 00003900 THREE DOTS ARE PLACED AT THE END OF THE SEQUENCE TO SHOW 00004000 THAT IT CONTINUES IN THE SAME PATTERN WITHOUT END. 00004100 ANOTHER EXAMPLE IS* 1,1,2,3,5,8,13,... 00004200 THERE ARE ESPECIALLY INTERESTING SEQUENCES, LIKE THE 00004300 ONE ABOVE WHICH IS CALLED A FIBONACCI SEQUENCE AND HAS 00004400 MANY INTERPRETATIONS IN NATURE. HOWEVER, FOR THE PRESENT 00004500 WE JUST WANT TO CREATE PATTERNS AND SEE HOW YOU 00004600 UNDERSTAND THEM. 00004700 UN WRITE THE FIRST THREE NUMERALS IN THE SEQUENCE; EACH 00004800 NUMERAL FOLLOWED BY A COMMA AND A SPACE. 00004900 UN YOU WILL BE TAKEN BACK FOR A REVIEW OF SEQUENCES 00005000 BR BACK 0000000H00005100 LA PROB3 00005200 QU HERE IS AN INTERESTING ONE: 1, 4, 9, 16, 25, 36, ... 00005300 WHAT IS THE NEXT NUMBER IN THE SEQUENCE. 00005400 CA 49 00005500 CB FORTY-NINE 00005600 CB FORTY NINE 00005700 TY VERY GOOD. THE PATTERN CAN BE THOUGHT OF AS TAKING THE 00005800 COUNTING NUMBERS, 1, 2, 3, 4, 5, 6, AND SO ON AND 00005900 MULTIPLYING EACH NUMBER BY ITSELF OR AS SQUARING IT. 00006000 UN TRY AGAIN. LOOK AT THE NUMBERS FOR A PATTERN. 00006100 QU HERE IS ONE THAT IS VERY CLOSELY RELATED TO THE ONE 00006200 ABOVE. 1, 8, 27, 64, ... WHAT IS THE NEXT NUMBER 00006300 IN THE SEQUENCE. 00006400 CA 125 00006500 TY EXCELLENT. I AM SURE THAT YOU SEE THE PATTERN IS TO TAKE 00006600 EACH COUNTING NUMBER AS A FACTOR THREE TIMES; OR TO CUBE 00006700 EACH COUNTING NUMBER. 00006800 UN TRY AGAIN. 00006900 UN YOU DID NOT LOOK AT THE NUMBERS; THE FIRST ONE IS 1, 00007000 THE SECOND NUMBER IS 8 WHICH EQUALS 2X2X2, THE THIRD 00007100 NUMBER IS 27, WHICH IS 3X3X3, THE FOURTH NUMBER IS 00007200 64 WHICH IS 4X4X4. NOW WHAT IS THE FIFTH NUMBER. 00007300 UN IF YOU GIVE UP TYPE HELP. 00007400 QU HERE IS A NEW ONE. 1, 4, 13, 40, 121, ... WHAT IS 00007500 THE NEXT NUMBER IF YOU ARE TOLD THAT IN THIS SEQUENCE 00007600 IT INVOLVED A MULTIPLICATION AND AN ADDITION. 00007700 CA 364 00007800 TY THAT IS CORRECT. YOU HAVE SEEN THAT THE RULE OR PATTERN 00007900 IS TO MULTIPLY THE NUMBER BY THREE AND ADD ONE. 00008000 UN THINK OF HOW EACH NUMBER IF FORMED FROM THE ONE BEFORE IT. 00008100 WRITE YOUR ANSWER NOW. 00008200 UN THE SEQUENCE IS 1, 4, 13, 40, 121, ... THINK ABOUT 00008300 MULTIPLYING EACH NUMBER BY THREE AND ADDING SOMETHING. 00008400 UN IF YOU GIVE UP TYPE HELP. 00008500 QU THESE CAN BE DONE WITH FRACTIONS TOO. CAN YOU FIGURE 00008600 THIS PATTERN: 1, 1/2, 1/4, ... WHAT WILL THE NEXT NUMBER BE. 00008700 CA 1/8 00008800 TY THAT IS CORRECT. YOU HAVE THE IDEA OF SEQUENCES AND CAN 00008900 CREATE PATTERNS OF YOUR OWN AND TRY THEM OUT ON YOUR 00009000 FRIENDS. 00009100 00009200 THIS IS THE END OF THIS COURSE. PLEASE REMEMBER WHAT YOU 00009300 HAVE LEARNED. 00009400 UN YOU ARE NOT THINKING 00009500 UN LOOK AT THE DENOMINATORS. EACH NUMERATOR IS 1, BUT THE 00009600 DENOMINATORS ARE CHANGING IN A VERY EASY WAY. 00009700 99 00009800