Computer Shopper 125/Computer Shopper CD-ROM Issue 125 (1998-07)(Dennis Publishing).iso/EuroMath/MathDemo/DataBase/learning/ID363.txt

Text File | 1996-10-22 | 3.9 KB | 272 lines

H@seeAlso 2difference method - single step
@seeAlso 2difference method - multiple step
@seeAlso 2difference method - multiplication
@seeAlso 2arithmetic progression
@seeAlso 2geometric progression


@animate FibRaiseLArm


@atGraphic 5,5
@Picture algebra\a010101.bmp



@PlaySoundFile \a1010101.wav



@At 0,5
#<number sequences#



@definition
@at 60,23
A set of numbers linked by a common
@At 10,
rule is known as a number sequence or pattern.




@prompt
@At 10,55
@keyPoint 9999,introduction


@animate FibLowerLArm

A number sequence can also be called a
#bprogression#. Each number in the sequence
is called a #Bterm#.

@PlaySoundFile \a1010102.wav
@PlaySoundFile \a1010103.wav

@Wait 0.5
@at ,+8
1st term 2nd term 3rd term 4th term 5th term . . .



@animate FibRaiseRArm,FibWaveRArm,FibWaveRArm,FibWaveRArm,FibLowerRArm



@Wait 0.25
      3,            ;
@Wait 0.25
6,          ;
@Wait 0.25
9,           ;
@Wait 0.25
12,         ;
@Wait 0.25
15     . . .


@Wait 0.5





@at 10,+8
Each term is linked to the next one in the
sequence by a rule.

For example in the above sequence the #brule#
could be :


@Wait 0.5
@at ,+8
#bAdd 3 to the last term to find the next#
#Bterm#.





@prompt
@keyPoint 9999,arithmetic progression
@animate FibSwordOut,FibWaveSword,FibWaveSword,FibWaveSword,FibSwordIn


     3,      ;
@Wait 0.25
6,      ;
@Wait 0.25
9,    ;
@Wait 0.25
12,     ;
@Wait 0.25
15,     ;
@Wait 0.25
18,     ;
@Wait 0.25
21   . . .


@Wait 0.5
@at 10,+8
#bRule : Add 3 to the last term to find the#
#bnext term.#


@Wait 0.5
@at ,+8
The simplest type of sequence where the next
term is found by adding a constant value to the
last term is known as an #barithmetic#
#Bprogression#.


@Wait 0.5


@PlaySoundFile \a1010104.wav


@at ,+8
This constant value is called the #bcommon#
#bdifference#.


@Wait 0.5
@at ,+8
In this case the common difference = #B3#.







@prompt
@keyPoint 9999,multiplying rules

@PlaySoundFile \a1010105.wav


@animate FibRaiseLArm,FibLowerLArm

      2,     ;
@Wait 0.25
4,     ;
@Wait 0.25
8,     ;
@Wait 0.25
16,      ;
@Wait 0.25
32,      ;
@Wait 0.25
64,      ;
@Wait 0.25
128

@Wait 0.5




@animate FibRaiseRArm,FibWaveRArm,FibLowerRArm


@at 10,+8
Can you think what the rule might be here?

@animate FibRaiseRArm,FibWaveRArm,FibWaveRArm,FibWaveRArm,FibLowerRArm

@at ,+8
@Wait 3

How about :
@at ,+8

@Wait 0.5
#bThe next term is found by multiplying#
#bthe last term by 2.#

@Wait 0.5


@at ,+8
A number sequence where the next term is
found by multiplying or dividing the last term by a
number is called a #bgeometric progression#.

@Wait 0.5

@PlaySoundFile \a1010106.wav



@at ,+8
The constant number used to multiply each term
is called the #bcommon ratio#.



@prompt
@keyPoint 9999,summary
#bSummary#
@Wait 0.75
@At ,+3
   *   #^A set of numbers linked by a #brule# is known
#tas ;
@At -1,
a ;
@At -1,
#bnumber sequence# ;
@At -1,
or ;
@At -1,
#Bprogression#.
@at 10,+3
@wait 0.75

   * #tEach number in the sequence is known as
#ta #bterm#
@at ,+3
@Wait 0.75

   * #tThe next term in the sequence can always
#tbe found by applying the rule ;
@At -1,
to ;
@At -1,
the ;
@At -1,
last ;
@At -1,
term
@at 10,+3
@Wait 0.75

   *#tIf the rule contains only addition or
#Tsubtraction the sequence is called an
#T#barithmetic# #bprogression#
@at ,+3
@Wait 0.75

   *#tIf the rule contains multiplication or division
#Tthe sequence is called a #bgeometric#
#T#Bprogression#.




'@at 5,235
'See also:
'#j4difference method - single step#
'#j4difference method - multiple step#
'#j4difference method - multiplication#
'#j4arithmetic progression#
'#j4geometric progression#
fference method - multiplication#
'#j4arithmetic progression#
'#j4geometric progression#