algebra 1 of 4 - unit 5 - day 2 - geometric sequences.notebook · 09/03/2015 · algebra 1 of 4...

Algebra 1 of 4 Unit 5 Day 2 Geometric Sequences.notebook

1

March 28, 2016

1) 5, 7, 9, 11, ...

2) 5, 5, 15, 25, 35, ...

3) 2, 4, 8, 16, 32, ...

For each sequence below:a) Find the common difference b) Determine the 10th term in by using the formula learned in our last class

DO NOW

Algebra I 03/30/16Aim: How is a geometric sequence different from an arithmetic sequence?HW #81: Geometric Sequence WS


2

March 28, 2016

1) 5, 7, 9, 11, ...

2) 5, 5, 15, 25, 35, ...

3) 2, 4, 8, 16, 32, ...

a10 = 5 + 2(10 1) = 23

a10 = 5 + 10(10 1) = 85

Can't do... no common difference!

For each sequence below:a) Find the common difference b) Determine the 10th term in by using the formula learned in our last class

Aim: How is a geometric sequence different from an arithmetic sequence?HW #81: Geometric Sequence WS


3

March 28, 2016

2 4 6 8 10 12 14 16 18 200

2, 4, 8, 16, 32, ...

5, 7, 9, 11, ...Common difference

vs.

Common ratio

2 4 6 8 10 12 14 16 18 20



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March 28, 2016

Geometric Sequence: A pattern of numbers which has a common ratio (multiplier) between the numbers

They can get bigger

or smaller



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March 28, 2016

Finding the common ratio...

Question: If the numbers in the sequence are decreasing, what kind of number must the common ratio be?

Partner Talk

1) 10, 30, 90, 270...

3) 500, 100, 20, 4...

Together

You always have to think of it as multiplication...not division!!!

2) 5, 15, 45, 135...



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March 28, 2016

REGENTS PREP



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March 28, 2016

The formula for finding a term in a geometric sequence is almost the same as in an arithmetic sequence.

an = a1 + d(n 1)

The term youwant to find The first term

of the sequenceThe common

difference between the terms

The number of the term you want to find (2nd, 5th, etc.)

an = a1 * r(n1)


of the sequence

The common ratio between

the terms


Multiplying over and over is represented with exponents:

3*3*3*3*3 = 35

Adding over and over is represented with multiplication:

3+3+3+3+3 = 5(3)



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March 28, 2016

TogetherWrite a formula and use it to find the 15th term in the given series... 81, 27, 9, 3 ...

Question: Is the 15th term going to be a big number or a small number?


an = a1 * r(n1)


of the sequence


the terms



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March 28, 2016


What does each term in the function rule for a geometric sequence represent?


10

March 28, 2016

For each of the following, write a formula representing the series and use the formula to find the 15th term.

1) 4, 12, 36, 108...

2) 20, 10, 5, 2.5 ...

3) 60, 55, 50, 45 ...


an = a1 * r(n1)


of the sequence


the terms


Assess as You Work

1

2

3

I got it!

I don't get it

I'm not sure


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March 28, 2016

1) 4, 12, 36, 108...

2) 20, 10, 5, 2.5 ...

3) 60, 55, 50, 45 ...

an = 4 * 3(n1)

an = 60 5(n1)

an =20 * 1/2(n1)

a15 = 4 * 3(14) = 19,131,876

a15 = 10

a15 = .00122



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March 28, 2016

Exit SlipWrite a rule and find the 8th term for the given sequence

3, 6, 12, 24 ...



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March 28, 2016

Exit SlipWrite a rule and find the 8th term for the given sequence

3, 6, 12, 24 ...



14

March 28, 2016

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algebra 1 of 4 - unit 5 - day 2 - geometric sequences.notebook · 09/03/2015 · algebra 1 of 4...

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