Day 7 - Geometric...

Day 7 ­ Geometric Sequences.notebook

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March 28, 2018

Feb 26­4:35 PM

Warm-Up 3/28/18

1. The population of stray cats at the gas station doubles every 4 months. After 12 months, how many cats are roaming around if there were initially 9 cats?

2. Find the value of $500 deposited for 20 years in an account paying 15% annual interest compounded quarterly.

Day 7 ­ Geometric Sequences.notebook

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Learning Objectives3/27/18

I can write explicit and recursive formulas for geometric sequences.

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Opening:

• What is a sequence• Sequences can be

finite or infinite. • Can you give me

examples of sequences?

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,or common ratio.

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Two ways to define sequences:1. Closed/Explicit:• Can directly find nth term • NOT required to list 1st term• Uses formula an = a1(r)n-1

for geometric sequences

2. Recursive:• Relates each term in the sequence to a

previous term• Must ALWAYS state 1st term• Requires formula that relates the nth

term to the (n-1)th term

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Examples - Finding the Nth Term

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Finding Terms Using an Explicit Rule

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Examples - Finding Terms Using a Recursive Rule

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Creating a Recursive Rule

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Class Work 3/27/18

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Closing 3/28/18

Geometric or Arithmetic?

Common ratio? Common difference?

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Mar 21­5:21 PM

-1, 6, -36, 216,... 35, 32, 29,26, ...

-3, -23, -43, -63, ....

-3, -15, -75, -375, ..

4, 16, 36, 64, ...

-34, -64, -94, -124,.

-7, -9, -11, -13,...

-1, 1, 4, 8, ...

1, -5, 25, -125, ...

9, 14, 19, 24, ...

21, 15, 9, ...

-4, 1, 6, 11, ...

7, -7, 7, -7, ...

1/2, 3/2, 5/2, ...

2, -3, -8, ...

1, 3, 9, 27, ...

2, 10, 50, ...

-17, -13, -9, ...

8, 3, -2, ...

12, -6, 3, 3/2, ...

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Closing: Class Discussion

» What name can also be given to the type of pattern produced in a geometric sequence?

» Do geometric sequences form an exponential pattern?

» When r is a proper fraction, do we have exponential decay or growth?

» Give me an example of a geometric sequence that represents exponential decay?