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Unit 3 Exponential Functions Name: __________________________ Lesson 2 Notes 1 Date: ___________________________ Directions: Fill in the blanks below as you watch Video 1. We are going to learn: what is a geometric sequence? what is a common ratio? How to continue a geometric sequence to find the next several terms how to write a geometric sequence in “now-next” form Let's Review: An arithmetic sequence is a pattern of numbers where you _____ the same amount to get the next term. example: 20, 18, 16, ____ , ____ , ____ common difference = _______ – _______ next = now + ____________ _______________ What is a geometric sequence? A geometric sequence is a pattern of numbers where you __________ the same amount to get the next term. example #1: 4, 12, 36, ____ , ____ , ____ What is the common ratio? The common ratio is the number you __________ by the term you have ____, in order to get the _______ term. To find the common ratio, take the ________ term and divide it by the ______ term. example #1: next = ______ common ratio = _____ now 1 Unit 3 Exponential Functions Lesson 2 Notes 1 Example #2 486, 162, 54 , ____ , ____ , ____ 1. Divide the “next” term by the “now” term: (If it’s a decimal, click MATH -> 1 -> ENTER.) 2. What is the common ratio? ______ 3. Multiply that ratio by the “now” term to find the next term. 4. The “now-next” form would be: Next = now x ______ “Now-Next” Form of a Geometric Sequence Next = now x ___________ _________ Example #3 3125 , 625 , 125 , ____ , ____ , ____ 1. Divide the “next” term by the “now” term: (If it’s a decimal, click MATH -> 1 -> ENTER.) 2. What is the common ratio? ______ 3. Multiply that ratio by the “now” term to find the next term. 4. The “now-next” form would be: Next = now x ______ 2 Unit 3 Exponential Functions Unit 3 Exponential Functions Lesson 2 Notes 1 Lesson 1 Notes 4 Example #4: You Try! 1 , 4 , 16 , ____ , ____ , ____ 1. Divide the “next” term by the “now” term: (If it’s a decimal, click MATH -> 1 -> ENTER.) 2. What is the common ratio? ______ 3. Multiply that ratio by the “now” term to find the next term. 4. The “now-next” form would be: Next = now x ______ Example #5: Ben’s Baseball Card Ben originally bought a baseball card for $400 hoping that it would increase in value. Unfortunately, the value of the card has decreased by half each year. If this decrease in value continues, what will the value of Ben’s baseball card be for the next 4 years? _____ , _____ , _____ , _____ , _____ Now – next form: ______ = _______ x _____ Example #6: Carolina Checkers Club The North Carolina Checkers Club keeps growing. It started with 2 members. At the end of the first year, it had grown to 4 members. At the end of the second yea, it had 8 members. If it continues to grow at this rate, how many members will it have the next 3 years? _____ , _____ , _____ , _____ , _____ Now – next form: ______ = _______ x _____ 3 Unit 3 Exponential Functions Lesson 2 Notes 1 What did we learn? A geometric sequence is a pattern of numbers that multiplies by the same amount each time. We call this amount the common ratio. To find the common ratio, divide the “next” term by the “now” term. To write a geometric sequence in “now-next” form: Next = now x common ratio 4