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Directions: Solve these problems using sequences and series. While there may be other methods for solving these problems, this practice is focused on applying sequences and series.
1. |
Richard has two parents, four grandparents, and so on, for a typical ancestor listing.
Write an explicit formula and a recursive formula for the number of ancestors Richard has if we go back n generations.
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2. |
A college lecture hall has 18 rows of seats. There are 40 seats in the first row. Each row, behind the first row, gains two additional seats.
a) How many seats are in the 8th row?
b) How many seats, in total, are in the lecture hall?
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3. |
Given the sequence -4, 0, 4, 8, 12, ...,
Zak devises a formula for the sum of n terms
of the sequence. His formula is:
Is this formula correct? Support your answer.
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4. |
There are currently 500 aphids in a vegetable garden.
If the number of aphids doubles every 2 hours, how many aphids will there be after 24 hours?
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5. |
Colleen complains that the hot tub in her hotel suite is not "hot". The hotel tells her 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?
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6. |
Justin's coach wants him to add stomach crunches to his routine. His coach has a plan to start with 10 crunches, and to increase the number by 5 each day for one week.
a) Write an explicit formula that can determine the daily number of crunches under this plan.
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b) Using a series formula, find the total number of crunches Justin will have completed in one week.
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7. |
During a geological expedition, an ore sample containing 500 mg of a radioactive material is discovered. It is determined that this 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.
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8. |
Ester didn't win the Clarksville Station Lottery of $21,000, but she was listed as the 8th winner. After the winner of the $21,000, each successive winner received $1,500 less than the previous winner.
a) Determine how much Ester won.
b) Determine how many winners there are in total.
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9. |
After knee surgery, Chad's doctor tells him to return to his jogging program slowly. The doctor suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that Chad increase the daily time by 6 minutes for that week. How many weeks will it be before Chad is up to jogging 60 minutes per day?
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10. |
An aging trough (tank) used for watering cattle is leaking. It loses 12 gallons of water a day. A filled trough contains 360 gallons of water.
a) Starting with a full trough, how many gallons are remaining in the trough 2 weeks later? Assume there are no cattle in the pasture during this time.
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b) At a cost of $2.08 per gallon, how much will it cost to replace the water lost? |
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11. |
From Geometry we know that the sum of the interior angles of a triangle is 180º, of a
quadrilateral is 360º and of a pentagon is 540º, and that this pattern continues.
a) Write an explicit sequential formula for this pattern.
b) Write a recursive sequential formula for this pattern.
c) Find the sum of the interior angles of a dodecagon (12 sides).
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