1. Patterns and Sequences sol 6.17 by k woodard and k norman

2. Arithmetic Sequence the same number each time 2, 4, 6, 8, …
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

3. Arithmetic Sequences 4, 7, 10, 13,… 27, 24, 21, 18,… 5, 20, 35, 50,…
Common difference: + 3
27, 24, 21, 18,…
Common difference: - 3
5, 20, 35, 50,…
Common difference: + 15

4. Arithmetic Sequences are Linear Patterns
When you graph the pattern it makes a line
It goes up or down gradually.

5. 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)

6. Geometric Sequence
4, 8, 16, 32, 64, 128,…
Common ratio: x 2
2000, 1000, 500, 250, 125, 62.5,…
Common ratio: 𝐱 ½
6, 24, 96, 384, 1536, 6144,…
Common ratio: x 4

7. Geometric Sequences are Exponential Patterns
When you graph the pattern it makes a steep curve
It goes up or down fast!

8. Arithmetic Geometric 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

9. 08 SOL 6.17*

10. 08 SOL 6.17*

11. 06 SOL 6.17

12. Powers of 10
exponent
base
Ten to the 3rd power
=10 x 10 x 10 = 1000

13. Powers of Base 10

14. 08 SOL

15. 08 SOL 6.21, 6.22*

16. Look for patterns
all around you

17. Square Numbers
Numbers that can be represented by dots in a square array.
1st four square numbers are depicted below:

18. Perfect Square Numbers!
Floor Tiles
Perfect Square Numbers!
𝟏 𝟐 = 1
𝟐 𝟐 = 4
𝟑 𝟐 = 9
𝟒 𝟐 = 16
𝟓 𝟐 = 25

20. Triangular Numbers
Numbers that can be represented by dots in a triangular array.
1st four triangular numbers are depicted below:

22. 1
, 3
, 6
, 10

24. 07 SOl

25. 08 SOL

26. 06 SOL

27. 07 SOL

28. Fibonacci Sequence

29. Fibonacci Sequence

30. 1+1 =2
1+2 =3
2+3 =5
3+5 =8
5+8 =13
mat-cast.com

34. Fibonacci Sequence

35. The Fab 5 1, 1, 2, 3, 5, 8, 13, 21, 34 Perfect Square Multiply n*n
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169
The Fab 5
Arithmetic
+ or – the common difference
2, 4, 6, 8, 10
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
Fibonacci
Add the last 2 to get the next
1, 1, 2, 3, 5, 8, 13, 21, 34
worksheet