Question 1

Find a recursive rule for the nth term of the sequence.
-The second and fifth terms of an arithmetic sequence are $- 5$ and 1 , respectively.

Accepted Answer

A)  $a _ { n } = a _ { n - 1 } + 2$ 
B)  $a _ { n } = a _ { n - 1 } - 3$ 
C)  $a _ { n } = a _ { n - 1 } + 5$ 
D)  $a _ { n } = a _ { n - 1 } + 3$ 
A)  $a _ { n } = a _ { n - 1 } + 2$ 
B)  $a _ { n } = a _ { n - 1 } - 3$ 
C)  $a _ { n } = a _ { n - 1 } + 5$ 
D)  $a _ { n } = a _ { n - 1 } + 3$

Question 2

Find the sum of the first n terms of the sequence.
-5, 20, 80, . . . ; n = 10

Accepted Answer

A)  6,990,505 
B)  1,747,625 
C)  1,398,101 
D)  - 4,194,303 
A)  6,990,505 
B)  1,747,625 
C)  1,398,101 
D)  - 4,194,303

Question 3

Solve the problem.
-Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 3 shirts chosen from the 10 shirts in his closet. In how many ways can this be done?

Accepted Answer

A)  1800 
B)  259,200 
C)  43,200 
D)  10,800 
A)  1800 
B)  259,200 
C)  43,200 
D)  10,800

Question 4

Evaluate.
-4P3

Accepted Answer

A)  4 
B)  2 
C)  12 
D)  24 
A)  4 
B)  2 
C)  12 
D)  24

Question 5

Find the sum of the first n terms of the sequence.
-7, 10, 13, 16, . . . ; n = 8

Accepted Answer

A)  171 
B)  112 
C)  140 
D)  152 
A)  171 
B)  112 
C)  140 
D)  152

Question 6

Determine whether the infinite geometric series converges. If the series converges, determine the limit.
-10 + 50 + 250 + 1250 + ...

Accepted Answer

A)  Converges; 1560 
B)  Diverges 
C)  Converges; 310 
D)  Converges; 7810 
A)  Converges; 1560 
B)  Diverges 
C)  Converges; 310 
D)  Converges; 7810

Question 7

Determine whether the sequence converges or diverges. If it converges, give the limit.
-$10,20,40,80 , \ldots$

Accepted Answer

A)  Converges; 150 
B)  Converges; 70 
C)  Converges; 310 
D)  Diverges 
A)  Converges; 150 
B)  Converges; 70 
C)  Converges; 310 
D)  Diverges

Question 8

Find the sum of the arithmetic sequence.
-$- 1,2,5,8,11,14,17$

Accepted Answer

A)  63 
B)  56 
C)  20 
D)  $- 7$ 
A)  63 
B)  56 
C)  20 
D)  $- 7$

Question 9

Write out the first five terms of the sequence.
-$$a _ { n } = n ^ { 2 } - n$$

Accepted Answer

A)  $1,4,9,16,25$ 
B)  $0,3,8,15,24$ 
C)  $0,2,6,12,20$ 
D)  $2,6,12,20,30$ 
A)  $1,4,9,16,25$ 
B)  $0,3,8,15,24$ 
C)  $0,2,6,12,20$ 
D)  $2,6,12,20,30$

Question 10

Use mathematical induction to prove the statement is true for all positive integers n.
-$$5 \cdot 7 + 6 \cdot 8 + 7 \cdot 9 + \ldots + 5 n ( 5 n + 2 ) = \frac { 5 n ( 5 n + 1 ) ( 10 n + 7 ) } { 6 }$$

Accepted Answer

To prove the given statement using mathe

Question 11

Tell whether permutations or combinations are being described.
-7 digits are selected (with possible repetition) to form a code for an alarm system.

Accepted Answer

A)  Combinations 
B)  Permutations 
A)  Combinations 
B)  Permutations

Question 12

Find an explicit rule for the nth term of the sequence.
-$4,12,36,108 , \ldots$

Accepted Answer

A)  $a _ { n } = 3 \cdot 4 ^ { n - 1 }$ 
B)  $a _ { n } = 4 \cdot 3 ^ { n }$ 
C)  $a _ { n } = 4 \cdot 3 ^ { n - 1 }$ 
D)  $a _ { n } = 4 \cdot 3 ^ { n + 1 }$ 
A)  $a _ { n } = 3 \cdot 4 ^ { n - 1 }$ 
B)  $a _ { n } = 4 \cdot 3 ^ { n }$ 
C)  $a _ { n } = 4 \cdot 3 ^ { n - 1 }$ 
D)  $a _ { n } = 4 \cdot 3 ^ { n + 1 }$

Question 13

Find the first six terms of the sequence.
-$$a _ { 1 } = 3 , a _ { n } = 5 \cdot a _ { n - 1 }$$

Accepted Answer

A)  $3,15,75,375,1875,9375$ 
B)  $3,15,20,25,30,35$ 
C)  $15,75,375,1875,9375,46,875$ 
D)  $0,5,15,20,25,30$ 
A)  $3,15,75,375,1875,9375$ 
B)  $3,15,20,25,30,35$ 
C)  $15,75,375,1875,9375,46,875$ 
D)  $0,5,15,20,25,30$

Question 14

Tell whether permutations or combinations are being described.
-10 pageant contestants are selected to be given awards and titles, the first being the winner, the second being the first runner-up, the third being the second runner-up, and so forth.

Accepted Answer

A)  Permutations 
B)  Combinations 
A)  Permutations 
B)  Combinations

Question 15

How many automobile license plates can be made involving 2 letters followed by either 3 or 4 digits?

Accepted Answer

A)  7,536,000 
B)  7,416,000 
C)  7,436,000 
D)  7,476,000 
A)  7,536,000 
B)  7,416,000 
C)  7,436,000 
D)  7,476,000

Question 16

Tell whether permutations or combinations are being described.
-14 students are selected to form a committee.

Accepted Answer

A)  Combinations 
B)  Permutations 
A)  Combinations 
B)  Permutations

Question 17

Find the coefficient of the given term in the binomial expansion.
-$x ^ { 3 } y ^ { 3 }$ term, $( x + y ) ^ { 6 }$

Accepted Answer

A)  1 
B)  60 
C)  15 
D)  20 
A)  1 
B)  60 
C)  15 
D)  20

Question 18

Find the coefficient of the given term in the binomial expansion.
-$x ^ { 7 } y ^ { 3 }$ term, $( x + y ) ^ { 10 }$

Accepted Answer

A)  604,800 
B)  86,400 
C)  120 
D)  7 
A)  604,800 
B)  86,400 
C)  120 
D)  7

Question 19

Evaluate.
-8!

Accepted Answer

A)  5040 
B)  20,160 
C)  80,640 
D)  40,320 
A)  5040 
B)  20,160 
C)  80,640 
D)  40,320

Question 20

Find an explicit rule for the nth term of the sequence.
-$$- 1 , - 5 , - 25 , - 125 , \ldots$$

Accepted Answer

A)  $a _ { n } = 5 \cdot - 1 ^ { n }$ 
B)  $a _ { n } = - 1 \cdot 5 ^ { n - 1 }$ 
C)  $a _ { n } = - 1 \cdot 5 ^ { n }$ 
D)  $a _ { n } = 5 \cdot - 1 ^ { n + 1 }$ 
A)  $a _ { n } = 5 \cdot - 1 ^ { n }$ 
B)  $a _ { n } = - 1 \cdot 5 ^ { n - 1 }$ 
C)  $a _ { n } = - 1 \cdot 5 ^ { n }$ 
D)  $a _ { n } = 5 \cdot - 1 ^ { n + 1 }$

Find a recursive rule for the nth term of the sequence. -The second and fifth terms of an arithmetic sequence are $- 5$ and 1 , respectively.

Find the sum of the first n terms of the sequence. -5, 20, 80, . . . ; n = 10

Solve the problem. -Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 3 shirts chosen from the 10 shirts in his closet. In how many ways can this be done?

Evaluate. -4P3

Find the sum of the first n terms of the sequence. -7, 10, 13, 16, . . . ; n = 8

Determine whether the infinite geometric series converges. If the series converges, determine the limit. -10 + 50 + 250 + 1250 + ...

Determine whether the sequence converges or diverges. If it converges, give the limit. - $10,20,40,80 , \ldots$

Find the sum of the arithmetic sequence. - $- 1,2,5,8,11,14,17$

Write out the first five terms of the sequence. - $a _ { n } = n ^ { 2 } - n$

Use mathematical induction to prove the statement is true for all positive integers n. - $5 \cdot 7 + 6 \cdot 8 + 7 \cdot 9 + \ldots + 5 n ( 5 n + 2 ) = \frac { 5 n ( 5 n + 1 ) ( 10 n + 7 ) } { 6 }$

Tell whether permutations or combinations are being described. -7 digits are selected (with possible repetition) to form a code for an alarm system.

Find an explicit rule for the nth term of the sequence. - $4,12,36,108 , \ldots$

Find the first six terms of the sequence. - $a _ { 1 } = 3 , a _ { n } = 5 \cdot a _ { n - 1 }$

Tell whether permutations or combinations are being described. -10 pageant contestants are selected to be given awards and titles, the first being the winner, the second being the first runner-up, the third being the second runner-up, and so forth.

How many automobile license plates can be made involving 2 letters followed by either 3 or 4 digits?

Tell whether permutations or combinations are being described. -14 students are selected to form a committee.

Find the coefficient of the given term in the binomial expansion. - $x ^ { 3 } y ^ { 3 }$ term, $( x + y ) ^ { 6 }$

Find the coefficient of the given term in the binomial expansion. - $x ^ { 7 } y ^ { 3 }$ term, $( x + y ) ^ { 10 }$

Evaluate. -8!

Find an explicit rule for the nth term of the sequence. - $- 1 , - 5 , - 25 , - 125 , \ldots$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 9: Discrete Mathematics

Find a recursive rule for the nth term of the sequence. -The second and fifth terms of an arithmetic sequence are −5- 5−5 and 1 , respectively.

Find the sum of the first n terms of the sequence. -5, 20, 80, . . . ; n = 10

Solve the problem. -Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 3 shirts chosen from the 10 shirts in his closet. In how many ways can this be done?

Evaluate. -4P3

Find the sum of the first n terms of the sequence. -7, 10, 13, 16, . . . ; n = 8

Determine whether the infinite geometric series converges. If the series converges, determine the limit. -10 + 50 + 250 + 1250 + ...

Determine whether the sequence converges or diverges. If it converges, give the limit. - 10,20,40,80,…10,20,40,80 , \ldots10,20,40,80,…

Find the sum of the arithmetic sequence. - −1,2,5,8,11,14,17- 1,2,5,8,11,14,17−1,2,5,8,11,14,17

Write out the first five terms of the sequence. - an=n2−na _ { n } = n ^ { 2 } - nan​=n2−n

Use mathematical induction to prove the statement is true for all positive integers n. - 5⋅7+6⋅8+7⋅9+…+5n(5n+2)=5n(5n+1)(10n+7)65 \cdot 7 + 6 \cdot 8 + 7 \cdot 9 + \ldots + 5 n ( 5 n + 2 ) = \frac { 5 n ( 5 n + 1 ) ( 10 n + 7 ) } { 6 }5⋅7+6⋅8+7⋅9+…+5n(5n+2)=65n(5n+1)(10n+7)​

Tell whether permutations or combinations are being described. -7 digits are selected (with possible repetition) to form a code for an alarm system.

Find an explicit rule for the nth term of the sequence. - 4,12,36,108,…4,12,36,108 , \ldots4,12,36,108,…

Find the first six terms of the sequence. - a1=3,an=5⋅an−1a _ { 1 } = 3 , a _ { n } = 5 \cdot a _ { n - 1 }a1​=3,an​=5⋅an−1​

Tell whether permutations or combinations are being described. -10 pageant contestants are selected to be given awards and titles, the first being the winner, the second being the first runner-up, the third being the second runner-up, and so forth.

How many automobile license plates can be made involving 2 letters followed by either 3 or 4 digits?

Tell whether permutations or combinations are being described. -14 students are selected to form a committee.

Find the coefficient of the given term in the binomial expansion. - x3y3x ^ { 3 } y ^ { 3 }x3y3 term, (x+y)6( x + y ) ^ { 6 }(x+y)6

Find the coefficient of the given term in the binomial expansion. - x7y3x ^ { 7 } y ^ { 3 }x7y3 term, (x+y)10( x + y ) ^ { 10 }(x+y)10

Evaluate. -8!

Find an explicit rule for the nth term of the sequence. - −1,−5,−25,−125,…- 1 , - 5 , - 25 , - 125 , \ldots−1,−5,−25,−125,…

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Find a recursive rule for the nth term of the sequence. -The second and fifth terms of an arithmetic sequence are $- 5$ and 1 , respectively.

Determine whether the sequence converges or diverges. If it converges, give the limit. - $10,20,40,80 , \ldots$

Find the sum of the arithmetic sequence. - $- 1,2,5,8,11,14,17$

Write out the first five terms of the sequence. - $a _ { n } = n ^ { 2 } - n$

Use mathematical induction to prove the statement is true for all positive integers n. - $5 \cdot 7 + 6 \cdot 8 + 7 \cdot 9 + \ldots + 5 n ( 5 n + 2 ) = \frac { 5 n ( 5 n + 1 ) ( 10 n + 7 ) } { 6 }$

Find an explicit rule for the nth term of the sequence. - $4,12,36,108 , \ldots$

Find the first six terms of the sequence. - $a _ { 1 } = 3 , a _ { n } = 5 \cdot a _ { n - 1 }$

Find the coefficient of the given term in the binomial expansion. - $x ^ { 3 } y ^ { 3 }$ term, $( x + y ) ^ { 6 }$

Find the coefficient of the given term in the binomial expansion. - $x ^ { 7 } y ^ { 3 }$ term, $( x + y ) ^ { 10 }$

Find an explicit rule for the nth term of the sequence. - $- 1 , - 5 , - 25 , - 125 , \ldots$