Question 1

A girl has three skirts, ten blouses and five sweaters. How many different skirt-blouse-sweater combinations can she wear?

Accepted Answer

A) 160 
B) 18 
C) 120 
D) 146 
E) 150

Question 2

Bode's sequence, defined by  can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 6th term of the sequence.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

A bicycle rider coasts downhill, traveling 7 feet the first second. In each succeeding second, the rider travels 4 feet farther than in the preceding second. If the rider reaches the bottom of the hill in 15 seconds, find the total distance traveled.

Accepted Answer

A) 525 feet 
B) 517 feet 
C) 529 feet 
D) 521 feet 
E) 513 feet

Question 4

A girl has three skirts, eight blouses and four sweaters. How many different skirt-blouse-sweater combinations can she wear?

Accepted Answer

A) 92 
B) 106 
C) 15 
D) 96 
E) 72

Question 5

Find the smallest positive integer j for which the statement is true.

Accepted Answer

A) 32 
B) 1,024 
C) 27 
D) 35 
E) 31

Question 6

Find the number.

Accepted Answer

A) 32 
B) 30 
C) 28 
D) 720 
E) 34

Question 7

Find the sum.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

A company is to distribute $29,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

Accepted Answer

A) $6,400, $5,800, $5,200, $4,600, $4,000 
B) $6,800, $6,700, $6,300, $5,900, $4,600 
C) $7,000, $6,500, $6,100, $5,700, $4,600 
D) $7,000, $6,400, $5,800, $5,200, $4,600 
E) $6,800, $6,600, $6,200, $5,800, $4,600

Question 9

Evaluate the expression. 6!0!

Accepted Answer

A) 24 
B) 5,040 
C) 720 
D) 0 
E) 1

Question 10

Express the sum in terms of n.  (Hint: Use the theorem on sums to write the sum as  . Next, use the following formulas  and the theorem on the sum of a constant.)

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Find the fifth term of the geometric sequence whose first two terms are 3 and 6.

Accepted Answer

A) 18 
B) 32 
C) 96 
D) 9 
E) 48

Question 12

Find the specified term of the arithmetic sequence that has the two given terms.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

A pile of logs has 28 logs in the bottom layer, 27 in the second layer, 26 in the third, and so on. The top layer contains 20 logs. Find the total number of logs in the pile.

Accepted Answer

A) 212 logs 
B) 432 logs 
C) 217 logs 
D) 214 logs 
E) 216 logs

Question 14

A committee of 4 men and 3 women is to be chosen from a group of 11 men and 5 women. Determine the number of different ways of selecting the committee.

Accepted Answer

A) 4 
B) 330 
C) 3,300 
D) 79,200

Question 15

Find the fourth partial sum for the given sequence.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Find the sum.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Find the number.

Accepted Answer

A) 10 
B) 6 
C) 8 
D) 40,320 
E) 12

Question 19

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Bode's sequence, defined by  can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 10: Sequences, Series and Probability

A girl has three skirts, ten blouses and five sweaters. How many different skirt-blouse-sweater combinations can she wear?

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 6th term of the sequence.

A bicycle rider coasts downhill, traveling 7 feet the first second. In each succeeding second, the rider travels 4 feet farther than in the preceding second. If the rider reaches the bottom of the hill in 15 seconds, find the total distance traveled.

A girl has three skirts, eight blouses and four sweaters. How many different skirt-blouse-sweater combinations can she wear?

Find the smallest positive integer j for which the statement is true.

Find the number.

Find the sum.

A company is to distribute $29,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

Evaluate the expression. 6!0!

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

Find the fifth term of the geometric sequence whose first two terms are 3 and 6.

Find the specified term of the arithmetic sequence that has the two given terms.

A pile of logs has 28 logs in the bottom layer, 27 in the second layer, 26 in the third, and so on. The top layer contains 20 logs. Find the total number of logs in the pile.

A committee of 4 men and 3 women is to be chosen from a group of 11 men and 5 women. Determine the number of different ways of selecting the committee.

Find the fourth partial sum for the given sequence.

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Find the sum.

Find the number.

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.