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 SEQUENCEMultiply or Divide

by the same number each timeThis is called the common ratioexamples1, 4, 16, 64, …

common ratio is x 4400, 200, 100, 50, …

common ratio is 2

GEOMETRIC SEQUENCE4, 8, 16, 32, 64, 128,…

Common ratio: x 2

2000, 1000, 500, 250, 125, 62.5,…Common ratio: 2

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, /2

Start at 3, x 3

Start at

390,625, /5

Start at

218,700, /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

http://www.fibonacci.name/

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