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Algebra Unit 5 Day 8 Geometric Sequences.notebook
1
February 15, 2017
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 02/15/17Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
2
February 15, 2017
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: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
3
February 15, 2017
Wednesdays and Fridays with Ms. Sims Room 207A
* Extension Lessons * Test Corrections
* Peer Tutoring * MakeUp Missing Work
Algebra Unit 5 Day 8 Geometric Sequences.notebook
4
February 15, 2017
Bulletin Board Bonaza!This Friday from 3:15 4:30PM
Food and Extra Credit Available
Three Volunteers Needed to Help Decorate
Algebra Unit 5 Day 8 Geometric Sequences.notebook
5
February 15, 2017
Tuesdays, Wednesdays, and ThursdaysRoom 207A During Lunch
Algebra Unit 5 Day 8 Geometric Sequences.notebook
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February 15, 2017
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
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
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February 15, 2017
Geometric Sequence: A pattern of numbers which has a common ratio (multiplier) between the numbers
They can get bigger
or smaller
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
8
February 15, 2017
Finding the Common Ratio
Question: If the numbers in the sequence are decreasing, what kind of number must the common ratio be?
1) 10, 30, 90, 270...
3) 500, 100, 20, 4...
You always have to think of it as multiplication...not division!!!
2) 5, 15, 45, 135...
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
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February 15, 2017
REGENTS PREP
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
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February 15, 2017
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)
The term youwant to find The first term
of the sequence
The common ratio between
the terms
The number of the term you want to find (2nd, 5th, etc.)
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)
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
11
February 15, 2017
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)
The term youwant to find The first term
of the sequence
The common ratio between
the terms
The number of the term you want to find (2nd, 5th, etc.)
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
12
February 15, 2017
What does each term in the function rule for a geometric sequence represent?
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
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February 15, 2017
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)
The term youwant to find The first term
of the sequence
The common ratio between
the terms
The number of the term you want to find (2nd, 5th, etc.)
Assess as You Work
1
2
3
I got it!
I don't get it
I'm not sure
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
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February 15, 2017
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 * ½(n1)
a15 = 4 * 3(14) = 19,131,876
a15 = 10
a15 = .00122
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Arithmetic (linear)!
Algebra Unit 5 Day 8 Geometric Sequences.notebook
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February 15, 2017
Exit SlipWrite a rule and find the 8th term for the given sequence
3, 6, 12, 24 ...
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
16
February 15, 2017
Exit SlipWrite a rule and find the 8th term for the given sequence
3, 6, 12, 24 ...
Aim: How is a geometric sequence different from an arithmetic sequence?HW: Geometric Sequence WS
Algebra Unit 5 Day 8 Geometric Sequences.notebook
17
February 15, 2017
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