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
ARITHMETIC SEQUENCES
4, 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
Linear
When you graph the pattern it makes a line
It goes up or down gradually.
GEOMETRIC SEQUENCE
Multiply
by 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 SEQUENCE
4,
8, 16, 32, 64, 128,…
 Common
2000,
1000, 500, 250, 125, 62.5,…
 Common
6,
ratio: x 2
ratio: 𝐱 ½
24, 96, 384, 1536, 6144,…
 Common
ratio: x 4
GEOMETRIC SEQUENCES ARE EXPONENTIAL PATTERNS
Exponent ial
When you graph the pattern it makes a steep curve
It goes up or down fast!
MAKE YOUR OWN PATTERNS
Arithmetic Geometric

Start at 1, rule: +2

Start at 1, rule: x 2

Start at 1000, -50

Start at 1000, x 1/2

Start at 12, +6

Start at 3, x 3

Start at 81, -9

Start at 390,625, x 1/5

Start at 13, +5

Start at 218,700, x 1/3

Start at 20, -4

Start at 1, x 4
08 SOL 6.17*
08 SOL 6.17*
06 SOL
6.17
POWERS OF 10
base
Ten

10
10
3
exponent
to the 3rd power
3
=10 x 10 x 10 = 1000
POWERS OF BASE 10
100  1
101  1*10  10
102  1*10*10  100
10  1*10*10*10  1, 000
3
104  1*10*10*10*10  10, 000
105  1*10*10*10*10*10  100, 000
08 SOL
08 SOL 6.21, 6.22*
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!
TRIANGULAR NUMBERS
 Numbers
that can be represented by dots in
a triangular array.

1st four triangular numbers are depicted below:
1
3
+2
6
+3
10
+4
http://collegian.csufresno.edu/2008/
04/18/chingy-for-change-a-causeon-pause-for-a-quick-game/
07 SOL
08 SOL
06 SOL
07 SOL
FIBONACCI SEQUENCE
http://www.fibonacci.name/
FIBONACCI SEQUENCE
mat-cast.com
FIBONACCI SEQUENCE
Perfect Square
Multiply n*n
Arithmetic
+ or – the common
difference
2, 4, 6, 8, 10
1, 4, 9, 16, 25, 36, 49, 64,
81, 100, 121, 144, 169
Triangular
Add one more each time
1, 3, 6, 10
Geometric
X or / the common ratio
2, 4, 8, 16, 32
1, 10, 100, 1000
worksheet
Fibonacci
Add the last 2 to get the
next
1, 1, 2, 3, 5, 8,
13, 21, 34