thursday­geometric sequences and series.notebook
January 22, 2014
Geometric Sequences and Series
Sequence
an ordered list of numbers
Series the sum of the terms in a sequence
geometric sequence
a sequence that uses multiplication to get from one term to the next. The sequence grows exponentially.
Jan 20­8:40 PM
Geometric Sequences and Series
To find any term of a geometric sequence use:
explicit
recursive
or
the first term of the sequence
is the common ratio (what we multiply by)
**to find divide any term by the one prior to it
the number of the term to find
an the nth term in a sequences
Jan 20­8:45 PM
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thursday­geometric sequences and series.notebook
January 22, 2014
Geometric Sequences and Series
Example: Find the common ratio for the sequence Answer: The common ratio is ­1/2 Jan 20­9:07 PM
Geometric Sequences and Series
Example: Find the common ration given
Answer: recall that r is the common ratio and in this case that is 3
Jan 20­9:10 PM
2
thursday­geometric sequences and series.notebook
January 22, 2014
Geometric Sequences and Series
Example: Find the 7th term of the sequence
2, 6, 18, 54, ...
an
term (n)
Jan 20­9:13 PM
Geometric Sequences and Series
Example: Find a8 for the sequence
0.5, 3.5, 24.5, 171.5, ... Jan 20­9:14 PM
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thursday­geometric sequences and series.notebook
January 22, 2014
Geometric Sequences and Series
Example: The third term of a geometric sequence is 3 and the sixth term is 1/9. Find the first term.
Jan 20­9:18 PM
Geometric Sequences and Series
Example: A ball is dropped from a height of 8 feet. The ball bounces to 80% of its previous height with each bounce. How high (to the nearest tenth of a foot) does the ball bounce on the fifth bounce?
Jan 20­9:19 PM
4
thursday­geometric sequences and series.notebook
January 22, 2014
Geometric Sequences and Series
what is the difference between an arithmetic sequence and a geometric sequence?
Jan 20­9:23 PM
Individual Practice:
What is the eleventh term of the geometric sequence 3, 6, 12, 24, ...?
What is the ninth term of the geometric sequence 81, 27, 9, 3, ... ?
Jan 20­10:12 PM
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thursday­geometric sequences and series.notebook
January 22, 2014
The fourth term of a geometric sequence is 27 and the seventh term is 1. What is the first term?
The first term of a geometric sequence is 192 and the fifth term is 0.75. What is the common ratio?
Jan 20­10:14 PM
You complain that the hot tub in your hotel suite is not hot enough.
The hotel tells you that they will increase the temperature by 10% each hour. a. Write an geometric sequence to determine the temperature of the water at any given time.
b. If the current temperature of the hot tub is 75º F, what will be the temperature of the hot tub after 3 hours, to the nearest tenth of a degree?
Jan 20­10:15 PM
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thursday­geometric sequences and series.notebook
January 22, 2014
A culture of bacteria doubles every 2 hours. There are 500 bacteria at the beginning.
a. Write an arithmetic sequence to determine the number of bacteria at any given time interval.
b. How many bacteria will there be after 24 hours?
Jan 20­10:15 PM
A mine worker discovers an ore sample containing 500 mg of radioactive material. It is discovered that the radioactive material has a half life of 1 day. Find the amount of radioactive material in the sample at the beginning of the 7th day. (show how you use a geometric sequence)
Jan 20­10:16 PM
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