 Sequences & Word Problems Terms of Use    Contact Person: Donna Roberts  1.
The Greek theater shown at the right has 30 seats in the first row of the center section. Each row behind the first row gains two additional seats.
How many seats are in the 5th row in the center section?

Choose: 36 38 40 44

2.
Billy is stacking alphabetic blocks in the pattern shown at the right. The number of blocks in each stack represents the terms in a sequence.
a) Which "rule" represents this sequence?
Choose:
 f (n) = n + 2 f (n) = n + 1 f (n) = n f (n) = 2n b)
In which stack will Billy place the letter "J" at the bottom of the stack?
Choose:
 8th stack 9th stack 10th stack 11th stack

3.
Mr. Carlson suffers from allergies. When allergy season arrives, his doctor recommends that he take 300 mg of his medication the first day, and decrease the dosage by one half each day for one week.
a) Which "rule" represents his medication doses for the week?
Choose:
 f (n) = 300•(½)n - 1 f (n) = (½)n - 1 f (n) = 300 + (½)n f (n) = (½)n b)
To the nearest milligram, what is the amount of medication Mr. Carlson will take on the 7th day?
Choose:
 19 mg 9 mg 38 mg 5 mg

4.
A pattern exists in the sum of the interior angles of polygons. The sum of the interior angles of a triangle is 180º, of a quadrilateral is 360º, and of a pentagon is 540º.
a) Which choice is a recursive formula for this pattern?
Choose:
 f (1) = 180;   f (n) = 180 • f (n - 1) f (1) = 180;   f (n) = f (n - 1) + 360 f (1) = 180;   f (n) = f (n + 1) + 180 f (1) = 180;   f (n) = f (n -1) + 180

b)
What is the sum of the interior angles of a nonagon?
Choose:
 900º 1080º 1260º 1440º 5.
Lanie has decided to add strength training to her exercise program. Her trainer suggests that she add weight lifting for 5 minutes during her routine for the first week. Each week thereafter, she is to increase the weight lifting time by 2 minutes.
a) Which formula represents this sequential increase in weight lifting time?
Choose:
 f (n) = 5n + 2 f (n) = 2n + 5 f (n) = 3n + 2 f (n) = 2n + 3 b)
If Lanie continues with this increase in weight lifting time, how many minutes will she be devoting to weight lifting in week 10?
Choose:
 23 25 32 52

6.
A research lab is to begin experimentation with a bacteria that doubles every 4 hours. The lab starts with 200 bacteria.
a) Which recursive formula represents the growth numbers of the bacteria?
Choose: f (1) = 200;   f (n) = f (n - 1) + 200 f (1) = 200;   f (n) = 4 • f (n - 1) f (1) = 200;   f (n) = 2 • f (n - 1) f (1) = 200;   f (n) = f (n -1) + 400

b)
How many bacteria will be present at the end of the 12th hour?
Choose:
 800 1,600 2,400 819,200

7.
Your father wants you to help him build a shed in the backyard. He says he will pay you \$10 for the first week and add an additional \$10.50 each week thereafter. The project will take 5 weeks.
How much money will you earn, in total, if you work for the 5 weeks? Choose:
 \$52 \$62 \$155 \$205

8.
The summer Olympics occur every four years. a) Which formula represents the years of the summer Olympics, starting with 2016?
Choose:
 f (n) = 2016 + 4(n + 1) f (n) = 4n + 2016 f (n) = 2016 + 4(n - 1) f (n) = 2016 + (n + 4)

b)
Starting with 2016, in which year will the 12th summer Olympics occur?
Choose:
 2056 2058 2060 2068 9.
Leonardo Pisano (Fibonacci) pondered the question: How many pairs of rabbits can be produced from a single pair of rabbits, in one year, under optimal conditions (none die, and the females always gives birth to one male and one female)? Rabbits must be one month old to reproduce, so only one pair exists again at the beginning of the 2nd month. At the end of the 2nd month, the female gives birth, leaving 2 pairs of rabbits at the beginning of the 3rd month. At the end of the 3rd month, the original pair produce another pair of newborns (while their earlier offspring mature), leaving 3 pairs to start the 4th month. The Fibonacci sequence is:
{1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...}, where each entry represents the number of pairs of rabbits at the beginning of each month.
a) Which statement describes the Fibonacci pattern to find successive terms?
Choose:
 multiply the previous two terms. add the previous two terms. multiply the previous term times 2. add 1 to the previous term. b)
How many pairs of rabbits will be present at the end of the 12th month (or the beginning of the 13th month)?
Choose:
 55 89 144 233

10.
Your grandmother gives you \$1000 to start a college book fund. She tells you she will add \$200 to the fund each month, if you will add \$5 each month.
a) Which "rule" generates a sequence of the monthly amounts in your college book fund?
Choose:
 f (n) = 1000 + 205(n - 1) f (n) = 205n + 795 f (1) = 1000; f (n) = f (n - 1) + 205 All three formulas generate this sequence. b) After how many months will the college book fund have \$5715? Choose: 12 18 24 36 NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use".