Question 1

Choose the one alternative that best completes the statement or answers the question.
-The 8 th term in the expansion of $( x - 2 y ) ^ { 13 }$

Accepted Answer

A)  $109,824 x ^ { 6 } y ^ { 8 }$ 
B)  $- 219,648 x ^ { 6 } y ^ { 7 }$ 
C)  $- 219,648 x ^ { 7 } y ^ { 6 }$ 
D)  $109,824 x ^ { 7 } y ^ { 6 }$ 
A)  $109,824 x ^ { 6 } y ^ { 8 }$ 
B)  $- 219,648 x ^ { 6 } y ^ { 7 }$ 
C)  $- 219,648 x ^ { 7 } y ^ { 6 }$ 
D)  $109,824 x ^ { 7 } y ^ { 6 }$

Question 2

Determine whether the sequence is arithmetic.
-$2,4,6,10,12 , \ldots$

Accepted Answer

A)  Arithmetic 
B)  Not arithmetic 
A)  Arithmetic 
B)  Not arithmetic

Question 3

Find the sum of the arithmetic sequence.
-{-6n + 2}, n = 36

Accepted Answer

A)  -3,636 
B)  -3,924 
C)  -3,762 
D)  -3,816 
A)  -3,636 
B)  -3,924 
C)  -3,762 
D)  -3,816

Question 4

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If
geometric, find the common ratio.
-$$\left\{ 3 n ^ { 2 } \right\}$$

Accepted Answer

A)  Geometric, $r = 3$ 
B)  Arithmetic, $\mathrm { d } = 3$ 
C)  Neither 
D)  Geometric, $r = \frac { 3 } { 2 }$ 
A)  Geometric, $r = 3$ 
B)  Arithmetic, $\mathrm { d } = 3$ 
C)  Neither 
D)  Geometric, $r = \frac { 3 } { 2 }$

Question 5

Express the sum using summation notation.
-$$\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$$

Accepted Answer

A)  $\sum _ { k = 1 } ^ { n } \frac { s ^ { k } } { k w }$ 
B)  $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$ 
C)  $\sum _ { k = 0 } ^ { n } \frac {  k } { k w }$ 
D)  $\sum _ { k = 0 } ^ { n } \frac { s ^ { k - 1 } } { k w }$ 
A)  $\sum _ { k = 1 } ^ { n } \frac { s ^ { k } } { k w }$ 
B)  $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$ 
C)  $\sum _ { k = 0 } ^ { n } \frac {  k } { k w }$ 
D)  $\sum _ { k = 0 } ^ { n } \frac { s ^ { k - 1 } } { k w }$

Question 6

Write the word or phrase that best completes each statement or answers the question.
-$$\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Determine whether the sequence is arithmetic.
-$2 , - 3 , - 8 , - 13 , - 18 , \ldots$

Accepted Answer

A)  Arithmetic 
B)  Not arithmetic 
A)  Arithmetic 
B)  Not arithmetic

Question 8

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of
summation.
-$$13 + 16 + 19 + 22 + \ldots + 37$$

Accepted Answer

A)  $\sum _ { k = 1 } ^ { 10 } 7 + 3 k$ 
B)  $\sum _ { k = 0 } ^ { 24 } 7 + 3 k$ 
C)  $\sum _ { k = 2 } ^ { 24 } 7 + 3 k$ 
D)  $\sum _ { k = 2 } ^ { 10 } 7 + 3 k$ 
A)  $\sum _ { k = 1 } ^ { 10 } 7 + 3 k$ 
B)  $\sum _ { k = 0 } ^ { 24 } 7 + 3 k$ 
C)  $\sum _ { k = 2 } ^ { 24 } 7 + 3 k$ 
D)  $\sum _ { k = 2 } ^ { 10 } 7 + 3 k$

Question 9

The sequence is defined recursively. Write the first four terms.
-$a _ { 1 } = 2$ and $a _ { n } = a _ { n - 1 } - 4$ for $n \geq 2$

Accepted Answer

A)  $- 4 , - 8 , - 12 , - 16$ 
B)  $2,6,10,14$ 
C)  $2,0 , - 4 , - 8$ 
D)  $2 , - 2 , - 6 , - 10$ 
A)  $- 4 , - 8 , - 12 , - 16$ 
B)  $2,6,10,14$ 
C)  $2,0 , - 4 , - 8$ 
D)  $2 , - 2 , - 6 , - 10$

Question 10

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-$$\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \ldots$$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 3 n - 2 }$ 
B)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = \frac { 1 } { n ^ { n - 1 } }$ 
D)  $a _ { n } = \frac { 1 } { n ^ { 2 } }$ 
A)  $a _ { n } = \frac { 1 } { 3 n - 2 }$ 
B)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = \frac { 1 } { n ^ { n - 1 } }$ 
D)  $a _ { n } = \frac { 1 } { n ^ { 2 } }$

Question 11

Determine whether the sequence is arithmetic.
-$2 , - 1 , - 4 , - 7 , - 10 , \ldots$

Accepted Answer

A)  Arithmetic 
B)  Not arithmetic 
A)  Arithmetic 
B)  Not arithmetic

Question 12

Choose the one alternative that best completes the statement or answers the question.
-A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?

Accepted Answer

A)  790 seats 
B)  1070 seats 
C)  1010 seats 
D)  1092 seats 
A)  790 seats 
B)  1070 seats 
C)  1010 seats 
D)  1092 seats

Question 13

Find the sum of the sequence.
-$$\sum _ { k = 2 } ^ { 5 } \frac { - 3 } { k }$$

Accepted Answer

A)  $- \frac { 77 } { 20 }$ 
B)  $- \frac { 45 } { 16 }$ 
C)  $\frac { 447 } { 10 }$ 
D)  $\frac { 17 } { 20 }$ 
A)  $- \frac { 77 } { 20 }$ 
B)  $- \frac { 45 } { 16 }$ 
C)  $\frac { 447 } { 10 }$ 
D)  $\frac { 17 } { 20 }$

Question 14

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-$$- 30 - 5 - \frac { 5 } { 6 } - \cdots$$

Accepted Answer

A)  Converges; $- 30$ 
B)  Converges; 6 
C)  Converges; $- 36$ 
D)  Converges; $- \frac { 215 } { 6 }$ 
A)  Converges; $- 30$ 
B)  Converges; 6 
C)  Converges; $- 36$ 
D)  Converges; $- \frac { 215 } { 6 }$

Question 15

Write out the sum. Do not evaluate.
-$$\sum _ { k = 1 } ^ { 6 } ( 5 k - 3 )$$

Accepted Answer

A)  $2 + 7 + 12 + 17 + 22 + 27 + \ldots$ 
B)  $1 + 2 + 7 + 12 + 17 + 22$ 
C)  60 
D)  $2 + 7 + 12 + 17 + 22 + 27$ 
A)  $2 + 7 + 12 + 17 + 22 + 27 + \ldots$ 
B)  $1 + 2 + 7 + 12 + 17 + 22$ 
C)  60 
D)  $2 + 7 + 12 + 17 + 22 + 27$

Question 16

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-$$\sum _ { k = 1 } ^ { \infty } 4 \left( \frac { 2 } { 3 } \right) ^ { k - 1 }$$

Accepted Answer

A)  Converges; 16 
B)  Converges; 4 
C)  Converges; 12 
D)  Converges; $\frac { 8 } { 3 }$ 
A)  Converges; 16 
B)  Converges; 4 
C)  Converges; 12 
D)  Converges; $\frac { 8 } { 3 }$

Question 17

Express the sum using summation notation.
-$$3 + 12 + 27 + \ldots + 75$$

Accepted Answer

A)  $\sum _ { k = 1 } ^ { 5 } 3 ^ { 2 } \mathrm { k }$ 
B)  $\sum _ { k = 0 } ^ { 5 } 3 k ^ { 2 }$ 
C)  $\sum _ { k = 1 } ^ { 5 } k ^ { 2 }$ 
D)  $\sum _ { k = 1 } ^ { 5 } 3 k ^ { 2 }$ 
A)  $\sum _ { k = 1 } ^ { 5 } 3 ^ { 2 } \mathrm { k }$ 
B)  $\sum _ { k = 0 } ^ { 5 } 3 k ^ { 2 }$ 
C)  $\sum _ { k = 1 } ^ { 5 } k ^ { 2 }$ 
D)  $\sum _ { k = 1 } ^ { 5 } 3 k ^ { 2 }$

Question 18

Find the indicated term of the sequence.
-The fourteenth term of the arithmetic sequence $25,19,13 , \ldots$

Accepted Answer

A)  $- 59$ 
B)  103 
C)  $- 53$ 
D)  $- 78$ 
A)  $- 59$ 
B)  103 
C)  $- 53$ 
D)  $- 78$

Question 19

Find the sum of the sequence.
-$$\sum _ { k = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { k }$$

Accepted Answer

A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 15 } { 16 }$ 
C)  $- \frac { 1 } { 16 }$ 
D)  $- \frac { 5 } { 16 }$ 
A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 15 } { 16 }$ 
C)  $- \frac { 1 } { 16 }$ 
D)  $- \frac { 5 } { 16 }$

Question 20

Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-$$\text { Show that the statement "n } { } ^ { 2 } - n + 3 \text { is a prime number" is true for } n = 1 \text {, but is not true for } n = 3 \text {. }$$

Accepted Answer

When @#LAT-DLM&, which is a prime number

Choose the one alternative that best completes the statement or answers the question. -The 8 th term in the expansion of $( x - 2 y ) ^ { 13 }$

Determine whether the sequence is arithmetic. - $2,4,6,10,12 , \ldots$

Find the sum of the arithmetic sequence. -{-6n + 2}, n = 36

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If geometric, find the common ratio. - $\left\{ 3 n ^ { 2 } \right\}$

Express the sum using summation notation. - $\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$

Write the word or phrase that best completes each statement or answers the question. - $\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }$

Determine whether the sequence is arithmetic. - $2 , - 3 , - 8 , - 13 , - 18 , \ldots$

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of summation. - $13 + 16 + 19 + 22 + \ldots + 37$

The sequence is defined recursively. Write the first four terms. - $a _ { 1 } = 2$ and $a _ { n } = a _ { n - 1 } - 4$ for $n \geq 2$

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - $\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \ldots$

Determine whether the sequence is arithmetic. - $2 , - 1 , - 4 , - 7 , - 10 , \ldots$

Choose the one alternative that best completes the statement or answers the question. -A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?

Find the sum of the sequence. - $\sum _ { k = 2 } ^ { 5 } \frac { - 3 } { k }$

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $- 30 - 5 - \frac { 5 } { 6 } - \cdots$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 6 } ( 5 k - 3 )$

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $\sum _ { k = 1 } ^ { \infty } 4 \left( \frac { 2 } { 3 } \right) ^ { k - 1 }$

Express the sum using summation notation. - $3 + 12 + 27 + \ldots + 75$

Find the indicated term of the sequence. -The fourteenth term of the arithmetic sequence $25,19,13 , \ldots$

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { k }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 11: Sequences; Induction; the Binomial Theorem

Choose the one alternative that best completes the statement or answers the question. -The 8 th term in the expansion of (x−2y)13( x - 2 y ) ^ { 13 }(x−2y)13

Determine whether the sequence is arithmetic. - 2,4,6,10,12,…2,4,6,10,12 , \ldots2,4,6,10,12,…

Find the sum of the arithmetic sequence. -{-6n + 2}, n = 36

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If geometric, find the common ratio. - {3n2}\left\{ 3 n ^ { 2 } \right\}{3n2}

Express the sum using summation notation. - 1w+s2w+s23w+…+sn−1nw\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }w1​+2ws​+3ws2​+…+nwsn−1​

Write the word or phrase that best completes each statement or answers the question. - (x−3x)4\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }(x−x​3​)4

Determine whether the sequence is arithmetic. - 2,−3,−8,−13,−18,…2 , - 3 , - 8 , - 13 , - 18 , \ldots2,−3,−8,−13,−18,…

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of summation. - 13+16+19+22+…+3713 + 16 + 19 + 22 + \ldots + 3713+16+19+22+…+37

The sequence is defined recursively. Write the first four terms. - a1=2a _ { 1 } = 2a1​=2 and an=an−1−4a _ { n } = a _ { n - 1 } - 4an​=an−1​−4 for n≥2n \geq 2n≥2

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - 11,14,19,116,125,…\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \ldots11​,41​,91​,161​,251​,…

Determine whether the sequence is arithmetic. - 2,−1,−4,−7,−10,…2 , - 1 , - 4 , - 7 , - 10 , \ldots2,−1,−4,−7,−10,…

Choose the one alternative that best completes the statement or answers the question. -A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?

Find the sum of the sequence. - ∑k=25−3k\sum _ { k = 2 } ^ { 5 } \frac { - 3 } { k }∑k=25​k−3​

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - −30−5−56−⋯- 30 - 5 - \frac { 5 } { 6 } - \cdots−30−5−65​−⋯

Write out the sum. Do not evaluate. - ∑k=16(5k−3)\sum _ { k = 1 } ^ { 6 } ( 5 k - 3 )∑k=16​(5k−3)

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - ∑k=1∞4(23)k−1\sum _ { k = 1 } ^ { \infty } 4 \left( \frac { 2 } { 3 } \right) ^ { k - 1 }∑k=1∞​4(32​)k−1

Express the sum using summation notation. - 3+12+27+…+753 + 12 + 27 + \ldots + 753+12+27+…+75

Find the indicated term of the sequence. -The fourteenth term of the arithmetic sequence 25,19,13,…25,19,13 , \ldots25,19,13,…

Find the sum of the sequence. - ∑k=14(−12)k\sum _ { k = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { k }∑k=14​(−21​)k

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Choose the one alternative that best completes the statement or answers the question. -The 8 th term in the expansion of $( x - 2 y ) ^ { 13 }$

Determine whether the sequence is arithmetic. - $2,4,6,10,12 , \ldots$

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If geometric, find the common ratio. - $\left\{ 3 n ^ { 2 } \right\}$

Express the sum using summation notation. - $\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$

Write the word or phrase that best completes each statement or answers the question. - $\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }$

Determine whether the sequence is arithmetic. - $2 , - 3 , - 8 , - 13 , - 18 , \ldots$

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of summation. - $13 + 16 + 19 + 22 + \ldots + 37$

The sequence is defined recursively. Write the first four terms. - $a _ { 1 } = 2$ and $a _ { n } = a _ { n - 1 } - 4$ for $n \geq 2$

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - $\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \ldots$

Determine whether the sequence is arithmetic. - $2 , - 1 , - 4 , - 7 , - 10 , \ldots$

Find the sum of the sequence. - $\sum _ { k = 2 } ^ { 5 } \frac { - 3 } { k }$

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $- 30 - 5 - \frac { 5 } { 6 } - \cdots$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 6 } ( 5 k - 3 )$

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $\sum _ { k = 1 } ^ { \infty } 4 \left( \frac { 2 } { 3 } \right) ^ { k - 1 }$

Express the sum using summation notation. - $3 + 12 + 27 + \ldots + 75$

Find the indicated term of the sequence. -The fourteenth term of the arithmetic sequence $25,19,13 , \ldots$

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { k }$