patterns and sequences sol 6.17 by k woodard and k norman

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

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