Question 1

Find the indicated sum.
-$$\frac { 1 } { 5 } + 1 + \frac { 9 } { 5 } + \ldots + 9$$

Accepted Answer

A)  $\frac { 552 } { 5 }$ 
B)  $\frac { 253 } { 5 }$ 
C)  66 
D)  $\frac { 276 } { 5 }$ 
A)  $\frac { 552 } { 5 }$ 
B)  $\frac { 253 } { 5 }$ 
C)  66 
D)  $\frac { 276 } { 5 }$

Question 2

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio.
--7, -11, -15, -19, . . .

Accepted Answer

A) yes, -12 
B) no 
C) yes, -4 
D) yes, 4 
A) yes, -12 
B) no 
C) yes, -4 
D) yes, 4

Question 3

Use the Binomial Theorem to expand the binomial.
-$\left( b ^ { 3 } - w ^ { 4 } \right) ^ { 6 }$

Accepted Answer

A)  $b ^ { 6 } - 6 b ^ { 5 } z + 15 b ^ { 4 } w ^ { 2 } - 20 b ^ { 3 } w ^ { 3 } + 15 b ^ { 2 } w ^ { 4 } - 6 a w ^ { 5 } + w ^ { 6 }$ 
B)  $b ^ { 18 } - 6 b ^ { 15 } w ^ { 4 } - 30 b ^ { 12 } w ^ { 8 } + 120 b ^ { 9 } w ^ { 12 } + 360 b ^ { 6 } w ^ { 16 } - 720 b ^ { 3 } w ^ { 20 } - 720 w ^ { 24 }$ 
C)  $b ^ { 18 } - w ^ { 24 }$ 
D)  $b ^ { 18 } - 6 b ^ { 15 } w ^ { 4 } + 15 b ^ { 12 } w ^ { 8 } - 20 b ^ { 9 } w ^ { 12 } + 15 b ^ { 6 } { } _ { w } ^ { 16 } - 6 b ^ { 3 } w ^ { 20 } + w ^ { 24 }$ 
A)  $b ^ { 6 } - 6 b ^ { 5 } z + 15 b ^ { 4 } w ^ { 2 } - 20 b ^ { 3 } w ^ { 3 } + 15 b ^ { 2 } w ^ { 4 } - 6 a w ^ { 5 } + w ^ { 6 }$ 
B)  $b ^ { 18 } - 6 b ^ { 15 } w ^ { 4 } - 30 b ^ { 12 } w ^ { 8 } + 120 b ^ { 9 } w ^ { 12 } + 360 b ^ { 6 } w ^ { 16 } - 720 b ^ { 3 } w ^ { 20 } - 720 w ^ { 24 }$ 
C)  $b ^ { 18 } - w ^ { 24 }$ 
D)  $b ^ { 18 } - 6 b ^ { 15 } w ^ { 4 } + 15 b ^ { 12 } w ^ { 8 } - 20 b ^ { 9 } w ^ { 12 } + 15 b ^ { 6 } { } _ { w } ^ { 16 } - 6 b ^ { 3 } w ^ { 20 } + w ^ { 24 }$

Question 4

Write the first four terms of the sequence.
-$$\mathrm { a } _ { \mathrm { n } } = \frac { ( - 1 ) ^ { n } } { ( \mathrm { n } + 1 ) ( \mathrm { n } + 4 ) }$$

Accepted Answer

A)  $- \frac { 1 } { 10 } , \frac { 1 } { 18 } , - \frac { 1 } { 28 } , \frac { 1 } { 40 }$ 
B)  $\frac { 1 } { 7 } , - \frac { 1 } { 9 } , \frac { 1 } { 11 } , - \frac { 1 } { 13 }$ 
C)  $\frac { 1 } { 10 } , - \frac { 1 } { 18 } , \frac { 1 } { 28 } , - \frac { 1 } { 40 }$ 
D)  $- \frac { 1 } { 7 } , \frac { 1 } { 9 } , - \frac { 1 } { 11 } , \frac { 1 } { 13 }$ 
A)  $- \frac { 1 } { 10 } , \frac { 1 } { 18 } , - \frac { 1 } { 28 } , \frac { 1 } { 40 }$ 
B)  $\frac { 1 } { 7 } , - \frac { 1 } { 9 } , \frac { 1 } { 11 } , - \frac { 1 } { 13 }$ 
C)  $\frac { 1 } { 10 } , - \frac { 1 } { 18 } , \frac { 1 } { 28 } , - \frac { 1 } { 40 }$ 
D)  $- \frac { 1 } { 7 } , \frac { 1 } { 9 } , - \frac { 1 } { 11 } , \frac { 1 } { 13 }$

Question 5

Find the indicated term of the sequence.
-$$\frac { 2 } { 3 } , - \frac { 1 } { 3 } , \frac { 1 } { 6 } , - \frac { 1 } { 12 } , \ldots ; \mathrm { a } 6$$

Accepted Answer

A)  $\frac { 1 } { 24 }$ 
B)  $\frac { 1 } { 30 }$ 
C)  $- \frac { 1 } { 96 }$ 
D)  $- \frac { 1 } { 48 }$ 
A)  $\frac { 1 } { 24 }$ 
B)  $\frac { 1 } { 30 }$ 
C)  $- \frac { 1 } { 96 }$ 
D)  $- \frac { 1 } { 48 }$

Question 6

Solve the problem.
-When students at the local university held a food drive, 1458 cans of food were collected on the first day of the drive, 486 the second day, 162 the third day, and so on. Find the total number of cans collected the first five days.

Accepted Answer

A) 2184 cans 
B) 2178 cans 
C) 2160 cans 
D) 3690 cans 
A) 2184 cans 
B) 2178 cans 
C) 2160 cans 
D) 3690 cans

Question 7

Find the probability.
-A bag contains 26 marbles, of which 3 are blue and 9 are green. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?

Accepted Answer

A)  $\frac { 23 } { 26 }$ 
B)  $\frac { 6 } { 13 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 3 } { 26 }$ 
A)  $\frac { 23 } { 26 }$ 
B)  $\frac { 6 } { 13 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 3 } { 26 }$

Question 8

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio.
-$$\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 } , \ldots$$

Accepted Answer

A)  yes, $\frac { 1 } { 2 }$ 
B)  no 
C)  yes, 2 
D)  yes, $\frac { 2 } { 3 }$ 
A)  yes, $\frac { 1 } { 2 }$ 
B)  no 
C)  yes, 2 
D)  yes, $\frac { 2 } { 3 }$

Question 9

Find the sum of the series.
-$$\sum _ { k = 2 } ^ { 5 } ( 4 k - 2 )$$

Accepted Answer

A)  48 
B)  36 
C)  26 
D)  42 
A)  48 
B)  36 
C)  26 
D)  42

Question 10

Provide an appropriate response.
-Given a geometric sequence such that $a _ { 1 } = 1$ and $a _ { 3 } = \frac { 1 } { 4 }$, find $a _ { 6 }$.

Accepted Answer

A)  $\frac { 1 } { 180 }$ 
B)  $\frac { 1 } { 240 }$ 
C)  $\frac { 1 } { 64 }$ 
D)  $\frac { 1 } { 32 }$ 
A)  $\frac { 1 } { 180 }$ 
B)  $\frac { 1 } { 240 }$ 
C)  $\frac { 1 } { 64 }$ 
D)  $\frac { 1 } { 32 }$

Question 11

Find the indicated sum.
-$$\sum _ { n = 1 } ^ { 37 } ( 2 n - 4 )$$

Accepted Answer

A)  1258 
B)  1221 
C)  1480 
D)  $1350.5$ 
A)  1258 
B)  1221 
C)  1480 
D)  $1350.5$

Question 12

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
-$$3 + \frac { 3 ^ { 2 } } { 2 } + \frac { 3 ^ { 3 } } { 3 } + \ldots + \frac { 3 ^ { n } } { n }$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { n } \frac { 3 ^ { n } } { i }$ 
B)  $\sum _ { i = 1 } ^ { n } \frac { 3 i } { i }$ 
C)  $\sum _ { i = 1 } ^ { n } \frac { 3 ^ { i } } { i }$ 
D)  $\sum _ { i = 1 } ^ { 3 } \frac { 3 ^ { i } } { i }$ 
A)  $\sum _ { i = 1 } ^ { n } \frac { 3 ^ { n } } { i }$ 
B)  $\sum _ { i = 1 } ^ { n } \frac { 3 i } { i }$ 
C)  $\sum _ { i = 1 } ^ { n } \frac { 3 ^ { i } } { i }$ 
D)  $\sum _ { i = 1 } ^ { 3 } \frac { 3 ^ { i } } { i }$

Question 13

Write a formula for the general term, or nth term, for the given sequence.
-$$1 , \frac { 2 } { 3 } , \frac { 1 } { 3 } , \frac { 2 } { 15 } , \ldots$$

Accepted Answer

A)  $a _ { n } = \frac { 2 n } { ( n + 1 ) ! }$ 
B)  $a _ { n } = \frac { 2 ^ { n + 1 } } { n ! }$ 
C)  $a _ { n } = \frac { 2 ^ { n } } { n ! }$ 
D)  $a _ { n } = \frac { 2 ^ { n } } { ( n + 1 ) ! }$ 
A)  $a _ { n } = \frac { 2 n } { ( n + 1 ) ! }$ 
B)  $a _ { n } = \frac { 2 ^ { n + 1 } } { n ! }$ 
C)  $a _ { n } = \frac { 2 ^ { n } } { n ! }$ 
D)  $a _ { n } = \frac { 2 ^ { n } } { ( n + 1 ) ! }$

Question 14

Use Pascal's triangle to expand the binomial.
-$$\left( x ^ { 3 } - 2 y ^ { 2 } \right) ^ { 5 }$$

Accepted Answer

A)  $x ^ { 15 } - 10 x ^ { 7 } y ^ { 2 } + 40 x ^ { 6 } y ^ { 4 } - 80 x ^ { 5 } y ^ { 5 } + 80 x ^ { 3 } y ^ { 6 } - 32 y ^ { 7 }$ 
B)  $x ^ { 15 } - 10 x ^ { 12 } y ^ { 2 } + 40 x ^ { 9 } y ^ { 4 } - 80 x ^ { 6 } y ^ { 6 } + 80 x ^ { 3 } y ^ { 8 } - 32 y 10$ 
C)  $x ^ { 15 } - 32 y ^ { 10 }$ 
D)  $x ^ { 15 } - 2 x ^ { 12 } y ^ { 2 } + 4 x ^ { 9 } y ^ { 4 } - 8 x ^ { 6 } y ^ { 6 } + 16 x ^ { 3 } y ^ { 8 } - 32 y ^ { 10 }$ 
A)  $x ^ { 15 } - 10 x ^ { 7 } y ^ { 2 } + 40 x ^ { 6 } y ^ { 4 } - 80 x ^ { 5 } y ^ { 5 } + 80 x ^ { 3 } y ^ { 6 } - 32 y ^ { 7 }$ 
B)  $x ^ { 15 } - 10 x ^ { 12 } y ^ { 2 } + 40 x ^ { 9 } y ^ { 4 } - 80 x ^ { 6 } y ^ { 6 } + 80 x ^ { 3 } y ^ { 8 } - 32 y 10$ 
C)  $x ^ { 15 } - 32 y ^ { 10 }$ 
D)  $x ^ { 15 } - 2 x ^ { 12 } y ^ { 2 } + 4 x ^ { 9 } y ^ { 4 } - 8 x ^ { 6 } y ^ { 6 } + 16 x ^ { 3 } y ^ { 8 } - 32 y ^ { 10 }$

Question 15

Solve the problem.
-John does 10 pushups on the first day of a 30-day month, and then increases the number of pushups by 3 pushups a day. How many pushups has he done by the end of the month?

Accepted Answer

A) 1595 pushups 
B) 1605 pushups 
C) 1695 pushups 
D) 1650 pushups 
A) 1595 pushups 
B) 1605 pushups 
C) 1695 pushups 
D) 1650 pushups

Question 16

Solve the problem.
-The kings are separated from a deck of standard playing cards and shuffled. One is randomly selected. What are the odds of drawing a black card?

Accepted Answer

A) 4 : 1 
B) 1 : 4 
C) 1 : 2 
D) 1 : 1 
A) 4 : 1 
B) 1 : 4 
C) 1 : 2 
D) 1 : 1

Question 17

Write the first four terms of the sequence.
-$$a _ { n } = \frac { n ^ { 5 } } { ( n + 1 ) ! }$$

Accepted Answer

A)  $\frac { 5 } { 2 } , \frac { 5 } { 3 } , \frac { 5 } { 4 } , 1$ 
B)  $\frac { 1 } { 2 } , \frac { 16 } { 3 } , \frac { 81 } { 8 } , \frac { 128 } { 15 }$ 
C)  $\frac { 5 } { 2 } , \frac { 5 } { 3 } , \frac { 5 } { 8 } , \frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 2 } , \frac { 16 } { 3 } , \frac { 81 } { 4 } , \frac { 256 } { 5 }$ 
A)  $\frac { 5 } { 2 } , \frac { 5 } { 3 } , \frac { 5 } { 4 } , 1$ 
B)  $\frac { 1 } { 2 } , \frac { 16 } { 3 } , \frac { 81 } { 8 } , \frac { 128 } { 15 }$ 
C)  $\frac { 5 } { 2 } , \frac { 5 } { 3 } , \frac { 5 } { 8 } , \frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 2 } , \frac { 16 } { 3 } , \frac { 81 } { 4 } , \frac { 256 } { 5 }$

Question 18

Write the first four terms of the sequence.
-$$a _ { n } = 4 ^ { n }$$

Accepted Answer

A) 4, 16, 64, 256 
B) 16, 64, 256, 1024 
C) 1, 4, 16, 64 
D) 1, 16, 81, 256 
A) 4, 16, 64, 256 
B) 16, 64, 256, 1024 
C) 1, 4, 16, 64 
D) 1, 16, 81, 256

Question 19

Solve the problem.
-Looking ahead to retirement, you sign up for automatic savings in a fixed-income 401K plan that pays 6.5% per year compounded annually. You plan to invest $2000 at the end of each year for the next 20 years. How much will your account have in it at the end of 20 years? Round to the nearest dollar.

Accepted Answer

A) $78,949 
B) $76,108 
C) $79,421 
D) $77,651 
A) $78,949 
B) $76,108 
C) $79,421 
D) $77,651

Question 20

Use Pascal's triangle to expand the binomial.
-$( x - 7 y ) ^ { 5 }$

Accepted Answer

A)  $x ^ { 5 } - 35 x ^ { 4 } y + 980 x ^ { 3 } y ^ { 2 } - 6860 x ^ { 2 } y ^ { 3 } + 12,005 x y ^ { 4 } - 16,807 y ^ { 5 }$ 
B)  $x ^ { 5 } - 35 x ^ { 4 } y + 490 x ^ { 3 } y ^ { 2 } - 3430 x ^ { 2 } y ^ { 3 } + 12,005 x y ^ { 4 } - 16,807 y ^ { 5 }$ 
C)  $x ^ { 5 } - 35 x ^ { 4 } y + 980 x ^ { 3 } y ^ { 2 } - 6860 x ^ { 2 } y ^ { 3 } + 12,005 x y ^ { 4 } - 7 y ^ { 5 }$ 
D)  $x ^ { 5 } - 35 x ^ { 4 } y + 490 x ^ { 3 } y ^ { 2 } - 3430 x ^ { 2 } y ^ { 3 } + 12,005 x y ^ { 4 } - 16,807$ 
A)  $x ^ { 5 } - 35 x ^ { 4 } y + 980 x ^ { 3 } y ^ { 2 } - 6860 x ^ { 2 } y ^ { 3 } + 12,005 x y ^ { 4 } - 16,807 y ^ { 5 }$ 
B)  $x ^ { 5 } - 35 x ^ { 4 } y + 490 x ^ { 3 } y ^ { 2 } - 3430 x ^ { 2 } y ^ { 3 } + 12,005 x y ^ { 4 } - 16,807 y ^ { 5 }$ 
C)  $x ^ { 5 } - 35 x ^ { 4 } y + 980 x ^ { 3 } y ^ { 2 } - 6860 x ^ { 2 } y ^ { 3 } + 12,005 x y ^ { 4 } - 7 y ^ { 5 }$ 
D)  $x ^ { 5 } - 35 x ^ { 4 } y + 490 x ^ { 3 } y ^ { 2 } - 3430 x ^ { 2 } y ^ { 3 } + 12,005 x y ^ { 4 } - 16,807$

Find the indicated sum. - $\frac { 1 } { 5 } + 1 + \frac { 9 } { 5 } + \ldots + 9$

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio. --7, -11, -15, -19, . . .

Use the Binomial Theorem to expand the binomial. - $\left( b ^ { 3 } - w ^ { 4 } \right) ^ { 6 }$

Write the first four terms of the sequence. - $\mathrm { a } _ { \mathrm { n } } = \frac { ( - 1 ) ^ { n } } { ( \mathrm { n } + 1 ) ( \mathrm { n } + 4 ) }$

Find the indicated term of the sequence. - $\frac { 2 } { 3 } , - \frac { 1 } { 3 } , \frac { 1 } { 6 } , - \frac { 1 } { 12 } , \ldots ; \mathrm { a } 6$

Solve the problem. -When students at the local university held a food drive, 1458 cans of food were collected on the first day of the drive, 486 the second day, 162 the third day, and so on. Find the total number of cans collected the first five days.

Find the probability. -A bag contains 26 marbles, of which 3 are blue and 9 are green. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio. - $\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 } , \ldots$

Find the sum of the series. - $\sum _ { k = 2 } ^ { 5 } ( 4 k - 2 )$

Provide an appropriate response. -Given a geometric sequence such that $a _ { 1 } = 1$ and $a _ { 3 } = \frac { 1 } { 4 }$ , find $a _ { 6 }$ .

Find the indicated sum. - $\sum _ { n = 1 } ^ { 37 } ( 2 n - 4 )$

Rewrite the series using summation notation. Use 1 as the lower limit of summation. - $3 + \frac { 3 ^ { 2 } } { 2 } + \frac { 3 ^ { 3 } } { 3 } + \ldots + \frac { 3 ^ { n } } { n }$

Write a formula for the general term, or nth term, for the given sequence. - $1 , \frac { 2 } { 3 } , \frac { 1 } { 3 } , \frac { 2 } { 15 } , \ldots$

Use Pascal's triangle to expand the binomial. - $\left( x ^ { 3 } - 2 y ^ { 2 } \right) ^ { 5 }$

Solve the problem. -John does 10 pushups on the first day of a 30-day month, and then increases the number of pushups by 3 pushups a day. How many pushups has he done by the end of the month?

Solve the problem. -The kings are separated from a deck of standard playing cards and shuffled. One is randomly selected. What are the odds of drawing a black card?

Write the first four terms of the sequence. - $a _ { n } = \frac { n ^ { 5 } } { ( n + 1 ) ! }$

Write the first four terms of the sequence. - $a _ { n } = 4 ^ { n }$

Use Pascal's triangle to expand the binomial. - $( x - 7 y ) ^ { 5 }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 9: Sequences and Series; Counting and Probability

Find the indicated sum. - 15+1+95+…+9\frac { 1 } { 5 } + 1 + \frac { 9 } { 5 } + \ldots + 951​+1+59​+…+9

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio. --7, -11, -15, -19, . . .

Use the Binomial Theorem to expand the binomial. - (b3−w4)6\left( b ^ { 3 } - w ^ { 4 } \right) ^ { 6 }(b3−w4)6

Write the first four terms of the sequence. - an=(−1)n(n+1)(n+4)\mathrm { a } _ { \mathrm { n } } = \frac { ( - 1 ) ^ { n } } { ( \mathrm { n } + 1 ) ( \mathrm { n } + 4 ) }an​=(n+1)(n+4)(−1)n​

Find the indicated term of the sequence. - 23,−13,16,−112,…;a6\frac { 2 } { 3 } , - \frac { 1 } { 3 } , \frac { 1 } { 6 } , - \frac { 1 } { 12 } , \ldots ; \mathrm { a } 632​,−31​,61​,−121​,…;a6