Solve the following problems dealing with
Arithmetic and Geometric Sequences and Series.
Look carefully at each question to determine with
"which" sequence you are working.
You may wish to have your graphing calculator handy.
1. 

You visit the Grand
Canyon and drop a penny off the edge of a cliff.
The distance the penny will fall is 16 feet the first
second, 48 feet the next second, 80 feet the third
second, and so on in an arithmetic sequence. What
is the total distance the object will fall in 6 seconds?



2. 
The sum of the
interior angles of a triangle is 180º, of a
quadrilateral is 360º and of a pentagon is 540º.
Assuming this pattern continues, find the sum of the
interior angles of a dodecagon (12 sides).




3. 
After knee surgery, your trainer tells you to return to
your jogging program slowly. He suggests jogging
for 12 minutes each day for the first week. Each
week thereafter, he suggests that you increase that time
by 6 minutes per day. How many weeks will it be
before you are up to jogging 60 minutes per day? 



4. 

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. 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? 


5. 
A culture of bacteria doubles every 2
hours. If there are 500 bacteria at the beginning,
how many bacteria will there be after 24 hours? 



6. 
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 7^{th }day.




