1. Geometric Sequences and Series
Chapter Dr. Guram
Algebra II /26/16

2. Focus Questions
How do we determine whether a given sequence is geometric?
How do we find the common ratio of a geometric sequence?
How do we write an expression for an geometric sequence and calculate the nth term?

3. Curriculum standards HSA-SSE.B.4
- Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
HSF-BF.A.1
- Write a function that describes a relationship between two quantities.
TN (Associated Tennessee Learning Expectations)
Use the formulas for the general term and summation of finite geometric … series.
Sources:
Spring Board Algebra 2 Textbook

4. Real World Examples Utilizing Geometric Series
What are examples of ways people use geometric series in real world situations?
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5. Real World Example of Geometric Series
Bank Account:  If you invest money in a compound-interest-earning account, then your initial investment will grow as a geometric sequence. Say you invest $1000 in an account that pays 5% interest compounded annually. That means that every year the value of your account will grow by 5%.
Viral videos: A video is watched by 10 people, 3 hours later 100 have watched it, 3 hours later 1000 people have watched it, etc. The video is being watched by a factor of 10 every 3 hours.

6. Academic language
Geometric Sequence: A sequence in which the ratio of any term to the previous term is constant.
Common Ratio: The constant ratio of consecutive terms of a geometric sequence.
Geometric Series: The expression formed by adding the terms of a geometric sequence.

7. Geometric Sequence Example 1

8. Geometric Sequence Example 1

9. Guided Practice Example

10. Geometric Sequence Key Concept

11. Example 2: Nth term

12. Example 2: Nth term

13. Geometric Sequence Example 3

14. Example 3 Answer

15. Example 3 Answer

16. Write a rule given two terms

17. Write a rule given two terms

18. Guided Practice Examples

19. Sum of a Finite Geometric Series

20. Sum of a Geometric Series

21. Sum of a Geometric Series

22. Geometric Sequence and Series in Real Life

23. Geometic Sequence and Series in Real Life

24. Review How do we determine whether a given sequence is geometric?
How do we find the common ratio of a geometric sequence?
How do we write an expression for a geometric sequence and calculate the nth term?

25. Review of terms Explain the mathematical term: Geometric Sequence.
Explain Geometric Series.
Give a real world example of Geometric Sequence/Series.

26. Class and HW Problems
12.3 Worksheet