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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
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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 ______
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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 _____
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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
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