1. Arithmetic and Geometric Sequences

2. Arithmetic Sequences
Every day a radio station asks a question for a prize of $150. If the 5th caller does not answer correctly, the prize money increased by $150 each day until someone correctly answers their question.

3. Arithmetic Sequences
Make a list of the prize amounts for a week (Mon - Fri) if the contest starts on Monday and no one answers correctly all week.

4. Arithmetic Sequences Monday : $150 Tuesday: $300 Wednesday: $450
Thursday: $600
Friday: $750

5. Arithmetic Sequences
These prize amounts form a sequence, more specifically each amount is a term in an arithmetic sequence. To find the next term we just add $150.

6. 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

7. What is the common difference?
The difference between each number. This determines what is added to each previous number to obtain the next number.
4, 8, 12, 16, 20…………..
4 is the common difference

8. Geometric Sequence
What if your pay check started at $100 a week and doubled every week. What would your salary be after four weeks?

9. GeometricSequence Starting $100. After one week - $200
After two weeks - $400
After three weeks - $800
After four weeks - $1600.
These values form a geometric sequence.

10. 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

11. What is the common ratio?
The number used to multiply by each previous number to obtain the next number.
2, 8, 32, 128, 512…………..
4 is the common ratio

12. Let’s Practice!

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

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

15. What is the next term in this sequence? 5, 20, 80, 320 , _____
Is this an arithmetic or geometric sequence?
What is the common ratio or difference?
What is the next term in this sequence? 5, 20, 80, 320 , _____ x4 x4 x4 x4
1,280

16. What is the next term in this sequence? 5, -1, -7 -13 , _____
Is this an arithmetic or geometric sequence?
What is the common ratio or difference?
What is the next term in this sequence? 5, -1, , _____ -6 -6 -6 -6
-19

17. What is the next term in this sequence? -3, 6, -12, 24 , _____
Is this an arithmetic or geometric sequence?
What is the common ratio or difference?
What is the next term in this sequence? -3, 6, -12, 24 , _____
X-2
X-2
X-2
X-2
-48

18. What is the next term in this sequence? -400,-380,-360,-340 , ____
Is this an arithmetic or geometric sequence?
What is the common ratio or difference?
What is the next term in this sequence? -400,-380,-360,-340 , ____
+20
+20
+20
+20
-320

19. What is the next term in this sequence? 100, 75, 50 , 25____
Is this an arithmetic or geometric sequence?
What is the common ratio or difference?
What is the next term in this sequence? , 75, 50 , 25____
-25
-25
-25
-25

20. What is the next term in this sequence? 12, -48, 192 , -768____
Is this an arithmetic or geometric sequence?
What is the common ratio or difference?
What is the next term in this sequence? 12, -48, 192 , -768____
x-4
x-4
x-4
x-4
3,072