patterns and sequences sol 6.17 by k woodard and k norman
DESCRIPTION
Patterns and Sequences sol 6.17 by k woodard and k norman. Arithmetic Sequence. Add or Subtract the same number each time This is called the common difference examples 2, 4, 6, 8, … common difference is + 2 1600, 1500, 1400, 1300, … common difference is -100. - PowerPoint PPT PresentationTRANSCRIPT
PATTERNS AND SEQUENCESSOL 6.17 BY K WOODARDAND K NORMAN
ARITHMETIC SEQUENCEAdd or Subtract
the same number each timeThis is called the common differenceexamples2, 4, 6, 8, …
common difference is + 21600, 1500, 1400, 1300, …
common difference is -100
ARITHMETIC SEQUENCES4, 7, 10, 13,…
Common difference: + 3
27, 24, 21, 18,…Common difference:- 3
5, 20, 35, 50,…Common difference: + 15
ARITHMETIC SEQUENCES ARE LINEAR PATTERNS
When you graph the pattern it makes a lineLinear
It goes up or down gradually.
GEOMETRIC SEQUENCEMultiplyby the same number each time (although it may appear as if you are dividing)
This is called the common ratio and is always represented by multiplication.
examples 1, 4, 16, 64, …
common ratio is 4 400, 200, 100, 50, …
common ratio is x 1/2 (dividing by 2 is the same as multiplying by
1/2)
GEOMETRIC SEQUENCE4, 8, 16, 32, 64, 128,…
Common ratio: x 2
2000, 1000, 500, 250, 125, 62.5,…Common ratio: ½
6, 24, 96, 384, 1536, 6144,…Common ratio: x 4
GEOMETRIC SEQUENCES ARE EXPONENTIAL PATTERNS
When you graph the pattern it makes a steep curveExponential
It goes up or down fast!
MAKE YOUR OWN PATTERNS
Start at 1, rule: x 2
Start at 1000, x 1/2
Start at 3, x 3
Start at 390,625, x
1/5
Start at 218,700, x
1/3
Start at 1, x 4
Start at 1, rule: +2
Start at 1000, -50
Start at 12, +6
Start at 81, -9
Start at 13, +5
Start at 20, -4
Arithmetic Geometric
08 SOL 6.17*
08 SOL 6.17*
06 SOL 6.17
POWERS OF 10
Ten to the 3rd power
=10 x 10 x 10 = 1000
310310
base
exponent
POWERS OF BASE 100
1
2
3
4
5
10
10 10
10 10*10
10 10*10*10
10 10*10*10*1
10
100
1,000
10,0
1
1*
1*
1*
1*
1
0
10 10*10*10*1
00
100,000* 0*10
08 SOL
08 SOL 6.21, 6.22*
Look for patternsall around you
SQUARE NUMBERS Numbers that can be represented by dots in a
square array. 1st four square numbers are depicted below:
FLOOR TILES
Perfect Square Numbers!
= 1 = 4 = 9 = 16 = 25
TRIANGULAR NUMBERS Numbers that can be represented by
dots in a triangular array.1st four triangular numbers are depicted
below:
1 3 6 10 +2 +3 +4
http://collegian.csufresno.edu/2008/04/18/chingy-for-change-a-cause-on-pause-for-a-quick-game/
1 , 3 , 6 , 10
07 SOL
08 SOL
06 SOL
07 SOL
FIBONACCI SEQUENCE
1+1 =2
1+2 =3
2+3 =5
3+5 =8
5+8 =13mat-cast.com
FIBONACCI SEQUENCE
Arithmetic+ or – the common difference
2, 4, 6, 8, 10
GeometricX or / the common ratio
2, 4, 8, 16, 321, 10, 100, 1000
Perfect SquareMultiply n*n
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169
TriangularAdd one more each time
1, 3, 6, 10FibonacciAdd the last 2 to get the next
1, 1, 2, 3, 5, 8, 13, 21, 34worksheet