Problem 6.17 Determine the axial forces in the BE members ...
Patterns and Sequences sol 6.17 by k woodard and k norman
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Transcript of 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 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
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