1. Advanced Math Topics Mrs. Mongold
Geometric Sequences
Advanced Math Topics
Mrs. Mongold

2. Reminder: Arithmetic Sequence
Definition:
Sequence in which the difference between any term and the term before it is a constant.
i.e. you are adding or subtracting the same number each time
Example:
2, 4, 6, 8, …
You are adding 2 to each term to get the next
10, 9, 8, 7, …
You are subtracting 1 from each term to get the next

3. Common Difference Definition: Example: The value of an – an-1
2, 4, 6, 8, …
4 – 2 = 2
6 – 4 = 2
8 – 6 = 2
d= 2

4. Geometric Sequence Definition: Example:
Sequence in which the ratio of any term to the term before it is a constant.
i.e. each term is multiplied or divided by the same number
Example:
2, 4, 8, 16, …
You multiply the previous term by 2 to get the next number
81, 27, 9, 3, …
You divide each term by 3 to get the next number

5. Common Ratio The value of an divided by an-1 Example: 2, 4, 8, 16, …
4/2 = 2
8/4 = 2
16/8 = 2
So common ratio r =2
If the pattern is dividing the common ratio is a fraction!!!

6. Geometric Sequence 0.05, 0.25, 1.25, 6.25, … Explicit Formula
an=a1rn-1
Pattern is previous term times 5 so r = 5
an=.05 (5)n-1
Recursive Formula
an=(an-1)r
Pattern is previous term times 5 so r = 5
an =(an-1)5
an=5(an-1)

7. Examples
1,-5, 25, -125, …
-4, -8/3, -16/9, -32/27…

8. More Examples
a1 = 4, r=3

9. More Examples
a1 = 8, r= ½

10. More Examples
a1 = 25, r= -5

11. More Examples

12. More Examples
100, 20, 4, 0.8, …

13. More Examples
1, 3, 6, 10, …

14. More Examples
12, 17, 22, 27, …

15. More Examples
0, 1, -1, 0, 1, -1 …

16. More Examples
25, 22, 19, 16, …

17. More Examples

18. Homework
Arithmetic Sequences HW #2
Geometric Sequences HW #3