Dugopolski’s 99College Algebra
Chapter 8 Test — Form A Name: ________________________
List the terms of each finite sequence.
1. 2. ( ) , ,
for 1 3 for 3 6
1. _________________________ 2. _________________________
Write a formula for the term of each infinite sequence. Do not use a recursion formula.
3. 4. 5. , , , , , , , , , , ,
3. _______________ 4. _______________ 5. ____________
Find the sum of each series. Round answers to the nearest hundredth, if necessary.
6. 7. ( ) ( )
6. _________________________ 7. _________________________
Solve each problem.
8. How many terms are there in the arithmetic sequence 2, 5, 8, , 293 ?
8. _________________________
9. How many different eleven-letter words” can be made from the letters in “MISSISSIPPI“?
9. _________________________
10. Find the 100 term in the sequence: , , , , .
10. _________________________
100 Form 8A
11. Write all of the terms of the binomial expansion for ( ) .
11. _______________________________________________________
12. Write the binomial expansion for ( ) using summation notation.
12. _________________________
13. If a pair of fair dice is rolled, what are the odds in favor of the sum of the numbers being 4?
13. _________________________
14. A collector of rare coins has 38 silver half-dollars. She plans on bringing 8 of them to
display at a local coin show. In how many ways could she choose the 8 coins for display?
14. _________________________
15. In a lottery, a person placing a bet randomly selects 3 digits from the digits 0 through 9,
without repetition allowed, and places them in order on a ticket. The winning 3-digit
number is to be selected that evening. What is the probability that the person will
choose the winning number?
15. _________________________
16. Use mathematical induction to prove that 3 5 (2 ) = for every
positive integer .
Dugopolski’s 101College Algebra
Chapter 8 Test — Form B Name: ________________________
List the terms of each finite sequence.
1. 2. ( ) , ,
for 1 3 for 3 6
1. _________________________ 2. _________________________
Write a formula for the term of each infinite sequence. Do not use a recursive formula.
3. 4. 5. , , , , , , , , , , ,
3. _______________ 4. _______________ 5. ___________
Find the sum of each series. Round answers to the nearest hundredth.
6. 7. ( )
6. _________________________ 7. _________________________
Solve each problem.
8. How many terms are there in the arithmetic sequence 2, 5, 8, , 299 ?
8. _________________________
9. How many different nine-letter words” can be made from the letters in “LOUISIANA”?
9. _________________________
10. Find the 98 term in the sequence: , , , , .
10. _________________________
102 Form 8B
11. Write all of the terms of the binomial expansion for ( ) .
11. ______________________________________________________
12. Write the binomial expansion for ( ) using summation notation.
12. _________________________
13. If a pair of fair dice is rolled, what are the odds in favor of the sum of the numbers being 5?
13. _________________________
14. A collector of fine art chooses to display her eight works by Dali in a group of three at any
one time. How many different display groupings does she have?
14. _________________________
15. In a lottery, a person placing a bet randomly selects 4 digits from the digits 0 through 9,
without repetition allowed, and places them in order on a ticket. The winning 4-digit
number is to be selected that evening. What is the probability that the person will choose
the winning number?
15. _________________________
16. Use mathematical induction to prove that 2 = for
every positive integer .
Dugopolski’s 103College Algebra
Chapter 8 Test — Form C Name: ________________________
List the terms of each finite sequence.
1. 2.
( ) , ,
for 1 3 for 3 6
1. _________________________ 2. _________________________
Write a formula for the term of each infinite sequence. Do not use a recursive formula.
3. 4. 5. 1, 16, 81, 256, 3, 7, 11, 15, 2, 8, 32, 128,
3. _______________ 4. _______________ 5. _____________
Find the sum of each series. Round answers to the nearest hundredth.
6. 7. ( )
6. _________________________ 7. _________________________
Solve each problem.
8. How many terms are there in the arithmetic sequence 1, 5, 9, , 353 ?
8. _________________________
9. A at a fine dining restaurant offers 3 choices for appetizer, 5 choices for entree’,prix fixe
and 4 choices for dessert. How many different variations on the meal areprix fixe
possible?
9. _________________________
10. Find the 100 term in the sequence: , , , , .
10. _________________________
104 Form 8C
11. Write all of the terms of the binomial expansion for ( ) .
11. ______________________________________________________
12. Write the binomial expansion for ( ) using summation notation.
12. _________________________
13. Five cards are dealt from a standard deck of 52 cards (4 cards of each rank in a deck).
What is the probability that the first two cards dealt are Aces and the next three are Kings?
13. _________________________
14. A collector of crystal animals has 57 pieces, but she can only display 5 at a time. How
many different sets of 5 could be chosen for display?
14. _________________________
15. A bag contains 20 candies: 3 cherry, 4 orange, 7 lemon and 6 grape. If two candies are
selected blindly, what is the probability that they are both the same flavor?
15. _________________________
16. Use mathematical induction to prove that =
for every positive integer .
Dugopolski’s 105College Algebra
Chapter 8 Test — Form D Name: ________________________
List the terms of each finite sequence.
1. 2.
, ,
for 1 3 for 3 6
1. _________________________ 2. _________________________
Write a formula for the term of each infinite sequence. Do not use a recursive formula.
3. 4. 5. , , , , , , , , 5, 8, 11, 14,
3. _______________ 4. _______________ 5. _____________
Find the sum of each series. Round answers to the nearest hundredth.
6. 7.( )
6. _________________________ 7. _________________________
Solve each problem.
8. How many terms are there in the arithmetic sequence 1, 5, 9, , 377?
8. _________________________
9. A at a fine dining restaurant offers 3 choices for appetizer, 4 choices for entree’,prix fixe
and 2 choices for dessert. How many different variations on the meal areprix fixe
possible?
9. _________________________
10. Find the 98 term in the sequence: , , , , .
10. _________________________
106 Form 8D
11. Write all of the terms of the binomial expansion for ( ) .
11. _____________________________________________________
12. Write the binomial expansion for ( ) using summation notation.
12. _________________________
13. Five cards are dealt from a standard deck of 52 cards (4 cards of each rank in a deck).
What is the probability that the first card dealt is an Ace, the next two are Kings, and the
final two are Jacks?
13. _________________________
14. A collector of crystal animals has 50 pieces, but she can only display 6 at a time. How
many different sets of 6 could be chosen for display?
14. _________________________
15. A bag contains 20 candies: 3 cherry, 4 orange, 7 lemon and 6 grape. If two candies are
selected blindly, what is the probability that they are both the same flavor?
15. _________________________
16. Use mathematical induction to prove that =
for every positive integer .
Dugopolski’s 107College Algebra
Chapter 8 Test — Form E Name: _________________________
Multiple Choice: Choose the best answer for each problem.
_____ 1. Find the first four terms for the sequence whose term is ( )!
a. 1, 2, 6, 12 b. 1, 2, 720, 12! c. 0, 2, 6, 24 d. 1, 2, 6, 24
_____ 2. Find all terms for a sequence whose term is = ( 1) , for 1 3.
a. 1, 4, 9 b. 1, 4, 9 c. 1, 4, 9 d. 1, 4, 9
_____ 3. Write a recursion formula for the sequence 1, , , ,
a. = b. = c. = ( ) d. = 2
_____ 4. Write the series using summation notation.
a. b. c. d.
_____ 5. Find the sum of the series: .
a. 68 b. 176 c. 198 d. 396
_____ 6. Write a formula for the term of the geometric sequence: , , , ,
a. b. c. d.
_____ 7. Find the number of terms of a geometric sequence with first term , common
ratio 0.5, and last term .
a. 8 b. 9 c. 10 d. 256
_____ 8. How many four-digit odd integers greater than 2000 can be formed using the
digits 0, 1, 2, and 3 at most once?
a. 1 b. 4 c. 6 d. 12
_____ 9. A pizza can be ordered in a medium or a large size. The toppings available are
pepperoni, ground meat, Canadian bacon, mushrooms, and green peppers.
How many different two-topping pizzas could be ordered? (Cheese is included
on all pizzas and not counted as one of the toppings.)
a. 10 b. 20 c. 40 d. 120
108 Form 8E
_____ 10. The Rolling Stones had 17 number one hit records, and the Beatles had 23. If
a disc jockey wants to play first a Stones hit and then a Beatles hit, how many
different pairs of songs (in that order) could be selected?
a. 391 b. 782 c. 1560 d. 1600
_____ 11. Ten students are available to help with a biology project. Five students are
needed to collect samples, 3 are needed to take measurements, and 2 are
needed to record the data. In how many ways can these jobs be assigned to
these 10 students?
a. 30 b. 300 c. 2520 d. 5040
_____ 12. Find the middle term in the expansion of ( ) .
a. 20 b. 5 c. 20 d.
_____ 13. If the odds in favor of event are , what is the probability that event
will occur?
a. b. c. d. 2
_____ 14. A survey of 100 people found that 30 people subscribe to , 50U.S. News
subscribe to , and 15 subscribe to both. How many subscribe toNewsweek
either or ?U.S. News Newsweek
a. 95 b. 85 c. 80 d. 65
_____ 15. Find .
a. 1 b. c. d.
_____ 16. Find the 100th term in the sequence: , , , ,
a. 702 b. 695 c. 202 d. 15
_____ 17. A bag contains 20 candies: 3 cherry, 4 orange, 7 lemon, and 6 grape. If two
candies are selected blindly, what is the probability that they are both the same
flavor?
a. b. 90 c. d.
_____ 18. If a pair of fair dice is rolled, what are the odds in favor of the sum being a 4?
a. 1 to 12 b. 4 to 11 c. 1 to 11 d. 1 to 18
Dugopolski’s 109College Algebra
Chapter 8 Test — Form F Name: _________________________
Multiple Choice: Choose the best answer for each problem.
_____ 1. Find the first three terms for the sequence whose term is ( )!
a. , , b. , , c. , , d. , ,
_____ 2. Find all terms for a sequence whose term is = ( ) , .
a. 1, 4, 9 b. 1, 4, 9 c. 1, 4, 9 d. 1, 4,9
_____ 3. Write a recursion formula for the sequence , , ,
a. = b. = c. = ( ) d. = 2
_____ 4. Find the sum ( ) .
a. 124 b. 44 c. 44 d. 124
_____ 5. Find the sum of the series: .
a. 383 b. 185 c. 163 d. 40
_____ 6. Write a formula for the term of the geometric sequence: , , , ,
a. b. c. d.
_____ 7. If $2000 is deposited at the beginning of a month into an account earning 6%
annual interest compounded monthly, then how much will be in the account at
the end of the 50 month?
a. $2120.00 b. $2150.00 c. $2566.45 d. $36,840.31
_____ 8. Find the number of terms of a geometric sequence with first term , common
ratio 0.5, and last term .
a. 8 b. 9 c. 10 d. 256
_____ 9. How many four-digit even integers greater than 3000 can be formed using the
digits 0, 1, 2, and 3 at most once?
a. 1 b. 4 c. 6 d. 12
_____ 10. If the odds in favor of event are , what is the probability that event
will occur?
a. b. c. d. 2
110 Form 8F
_____ 11. A pizza can be ordered in small, medium or large size. The toppings available
are pepperoni, roasted garlic, tomatoes, mushrooms, green peppers, and
onions. How many different two-topping pizzas could be ordered? (Cheese is
included on all pizzas and not counted as one of the toppings.)
a. b. c. d.
_____ 12. Eight students are available to help with a biology project. Four students are
needed to collect samples, 3 are needed to take measurements, and 1 is
needed to record the data. In how many ways can these jobs be assigned to
these 8 students?
a. 40,320 b. 6,720 c. 280 d. 15
_____ 13. Find the fourth term in the expansion of ( ) .
a. b. c. d.
_____ 14. A survey of people found that people subscribe to , U.S. News
subscribe to , and 15 subscribe to both. How many subscribe toNewsweek
neither one?
a. b. c. d.
_____ 15. Find .
a. 1 b. c. d.
_____ 16. Find the th term in the sequence: , , , ,
a. b. c. d.
_____ 17. A bag contains candies: cherry, orange, lemon, and grape. If two
candies are selected blindly, what is the probability that they are both the same
flavor?
a. b. c. d.
_____ 18. If a pair of fair dice is rolled, what are the odds in favor of the sum of the
numbers being a ?
a. to b. to c. to d. to
Dugopolski’s 127College Algebra
Chapter Test Keys
CHAPTER 8
Form A:
128 Chapter 8 Test Key