1. Sequences

2. What is a sequence? What is a term?
A list of numbers in a certain order.
What is a term?
One of the numbers in the sequence.

3. What is an arithmetic sequence?
A sequence in which each term is found by ADDING the same number to the previous term.
4, 8, , 16, 20………….. +4 +4 +4 +4

4. What is the common difference?
The difference between each number, or what you add each time.
4, 8, 12, 16, 20…………..
4 is the common difference
How do you find it?
The 2nd term minus the 1st term.

5. Arithmetic Sequence the same number each time 2, 4, 6, 8, …
Add
the same number each time
This is called the common difference
examples
2, 4, 6, 8, …
common difference is 2
50, 40, 30, 20…
common difference is -10

6. 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

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

8. What is a geometric sequence?
A sequence in which each term can be found by MULTIPLYING the previous term by the same number.
3, 9, , 81, ………….. x3 x3 x3 x3

9. What is the common ratio?
The ratio between each number in the sequence, or what you multiply by each time.
2, 8, 32, 128, 512…………..
4 is the common ratio
How do you find it?
The 2nd term divided by the 1st term.

10. Geometric Sequence by the same number each time 1, 4, 16, 64, …
Multiply
by the same number each time
This is called the common ratio
examples
1, 4, 16, 64, …
common ratio is x 4
400, 200, 100, 50, …
common ratio is x 𝟏 𝟐 or x o.5

11. Geometric Sequence
4, 8, 16, 32, 64, 128,…
Common ratio: x 2
2000, 1000, 500, 250, 125, 62.5,…
Common ratio: x ½ or x 0.5
6, 24, 96, 384, 1536, 6144,…
Common ratio: x 4

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

13. Arithmetic Geometric Make your own patterns 1st term: 1, n + 2

14. terms that are next to each other
Consecutive Terms:
terms that are next to each other
Variable Expression:
can show the rule of a pattern
Examples:
2, 4, 6, 8… n , 6, 4, 2… n + (-2)
2, 4, 8, 16… 2n 16, 8, 4, 2… 0.5n

15. Is this an arithmetic or geometric sequence?
10, 15, 20, 25, 30……
Arithmetic Sequence +5
5 is the common difference 1

16. Is this an arithmetic or geometric sequence?
2, 12, 72, 432, 2,592……
Geometric Sequence x6
6 is the common ratio

17. What is the next term in this sequence? 5, 20, 80, 320 , _____
1,280

18. What is the next term in this sequence? 5, -1, -7 -13 , _____-6 -6 -6 -6
-19

19. What is the next term in this sequence? -3, 6, -12, 24 , _____
-48

20. What is the next term in this sequence? -400,-380,-360,-340 , ____
+20
+20
+20
+20
-320

21. What is the next term in this sequence? 100, 75, 50 , 25____
-25
-25
-25
-25

22. What is the next term in this sequence? 12, -48, 192 , -768____
3,072