Geometric Sequences and Series Chapter 12-3 Dr. Guram Algebra II 2/26/16

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?

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 3103.3.4 (Associated Tennessee Learning Expectations) Use the formulas for the general term and summation of finite geometric … series. Sources: http://www.corestandards.org/Math/Content/HSA/CED/A/1/ Spring Board Algebra 2 Textbook

Real World Examples Utilizing Geometric Series What are examples of ways people use geometric series in real world situations? ???

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.

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.

Geometric Sequence Example 1

Geometric Sequence Example 1

Guided Practice Example

Geometric Sequence Key Concept

Example 2: Nth term

Example 2: Nth term

Geometric Sequence Example 3

Example 3 Answer

Example 3 Answer

Write a rule given two terms

Write a rule given two terms

Guided Practice Examples

Sum of a Finite Geometric Series

Sum of a Geometric Series

Sum of a Geometric Series

Geometric Sequence and Series in Real Life

Geometic Sequence and Series in Real Life

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?

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

Class and HW Problems 12.3 Worksheet