Question 1

Write out the first five terms of the sequence.
-$$\left\{ \frac { ( 2 n - 1 ) ! } { n ! } \right\}$$

Accepted Answer

A)  $2,6,40,1260,72,576$ 
B)  $1,6,40,1260,72,576$ 
C)  $2,3,20,210,3024$ 
D)  $1,3,20,210,3024$ 
A)  $2,6,40,1260,72,576$ 
B)  $1,6,40,1260,72,576$ 
C)  $2,3,20,210,3024$ 
D)  $1,3,20,210,3024$

Question 2

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-$$\sum _ { \mathrm { k } = 1 } ^ { 5 } 4 ( 3 ) ^ { \mathrm { k } }$$

Accepted Answer

A)  93 
B)  480 
C)  2,460 
D)  1,452 
A)  93 
B)  480 
C)  2,460 
D)  1,452

Question 3

Express the sum using summation notation.
-$$2 ^ { 3 } + 3 ^ { 3 } + 4 ^ { 3 } + \cdots + 8 ^ { 3 }$$

Accepted Answer

A) 
$\sum _ { k = 1 } ^ { 8 } k ^ { 3 }$ 
B) 
$\sum _ { k = 3 } ^ { 8 } ( k - 1 ) ^ { 3 }$ 
C) 
$\sum _ { k = 2 } ^ { 8 } k ^ { 3 }$ 
D) 
$\sum _ { k = 2 } ^ { n } k ^ { 3 }$ 
A) 
$\sum _ { k = 1 } ^ { 8 } k ^ { 3 }$ 
B) 
$\sum _ { k = 3 } ^ { 8 } ( k - 1 ) ^ { 3 }$ 
C) 
$\sum _ { k = 2 } ^ { 8 } k ^ { 3 }$ 
D) 
$\sum _ { k = 2 } ^ { n } k ^ { 3 }$

Question 4

Choose the one alternative that best completes the statement or answers the question.
-A bicycle wheel rotates 500 times in a minute as long as the rider is pedalling. If the rider stops pedalling, the wheel starts to slow down. Each minute it will rotate only 4/5 as many times as in the preceding minute. How
Many times will the wheel rotate in the 4th minute after the rider's feet leave the pedals? Round your answer to
The nearest unit.

Accepted Answer

A)  0 times 
B)  158 times 
C)  211 times 
D)  8 times 
A)  0 times 
B)  158 times 
C)  211 times 
D)  8 times

Question 5

Write out the first five terms of the sequence.
-$$\left\{ \frac { n } { n ^ { 2 } + 2 } \right\}$$

Accepted Answer

A)  $\frac { 1 } { 4 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
B)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$ 
C)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
D)  $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
A)  $\frac { 1 } { 4 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
B)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$ 
C)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
D)  $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$

Question 6

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-$0,2,6,12,20 , \ldots$

Accepted Answer

A)  $a _ { n } = 4 n - 6$ 
B)  $a _ { n } = 2 ^ { n - 1 } - 1$ 
C)  $a _ { n } = n ^ { 2 } - n$ 
D)  $a _ { n } = 2 n - 2$ 
A)  $a _ { n } = 4 n - 6$ 
B)  $a _ { n } = 2 ^ { n - 1 } - 1$ 
C)  $a _ { n } = n ^ { 2 } - n$ 
D)  $a _ { n } = 2 n - 2$

Question 7

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.
-$$1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

Accepted Answer

First we show that the statement is true

Question 8

Find the sum of the sequence.
-$$\sum _ { k = 1 } ^ { 5 } ( \mathrm { k } + 1 )$$

Accepted Answer

A)  14 
B)  20 
C)  6 
D)  8 
A)  14 
B)  20 
C)  6 
D)  8

Question 9

Express the sum using summation notation.
-$$\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }$$

Accepted Answer

A) 
$$\sum _ { k = 1 } ^ { n } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$$ 
B) 
$$\sum _ { \mathrm { k } = 1 } ^ { 14 } ( - 1 ) ^ { ( \mathrm { k } + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { \mathrm { k } }$$ 
C) 
$$\sum _ { k = 1 } ^ { 13 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { \mathrm { k } }$$ 
D)

$\sum _ { k = 1 } ^ { 13 } \left( \frac { 4 } { 5 } \right) ^ { k }$ 
A) 
$$\sum _ { k = 1 } ^ { n } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$$ 
B) 
$$\sum _ { \mathrm { k } = 1 } ^ { 14 } ( - 1 ) ^ { ( \mathrm { k } + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { \mathrm { k } }$$ 
C) 
$$\sum _ { k = 1 } ^ { 13 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { \mathrm { k } }$$ 
D)

$\sum _ { k = 1 } ^ { 13 } \left( \frac { 4 } { 5 } \right) ^ { k }$

Question 10

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-$$\frac { 1 } { 5 } + \frac { 2 } { 5 } + \frac { 2 ^ { 2 } } { 5 } + \frac { 2 ^ { 3 } } { 5 } + \cdots + \frac { 2 ^ { 13 } } { 5 }$$

Accepted Answer

A)  $3276.6$ 
B)  $6553.2$ 
C)  $6553.4$ 
D)  $3276.4$ 
A)  $3276.6$ 
B)  $6553.2$ 
C)  $6553.4$ 
D)  $3276.4$

Question 11

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-$$\frac { 1 } { 7 } , \frac { 1 } { 9 } , \frac { 1 } { 11 } , \frac { 1 } { 13 }$$

Accepted Answer

A)  2 
B)  $\frac { 1 } { 2 }$ 
C)  $2 \frac { 1 } { 2 }$ 
D)  Not geometric 
A)  2 
B)  $\frac { 1 } { 2 }$ 
C)  $2 \frac { 1 } { 2 }$ 
D)  Not geometric

Question 12

Expand the expression using the Binomial Theorem.
-$( w - s ) ^ { 6 }$

Accepted Answer

A)  $w ^ { 6 } - 6 w ^ { 5 } s + 15 w ^ { 4 } s ^ { 2 } - 20 w ^ { 3 } s ^ { 3 } + 15 w ^ { 2 } s ^ { 4 } - 6 w s ^ { 5 } + s ^ { 6 }$ 
B)  $w ^ { 6 } - 8 w ^ { 5 } s + 17 w ^ { 4 } s ^ { 2 } - 22 w ^ { 3 } s ^ { 3 } + 17 w ^ { 2 } s ^ { 4 } - 8 w s ^ { 5 } + s ^ { 6 }$ 
C)  $w ^ { 6 } - s ^ { 6 }$ 
D)  $w ^ { 6 } - 6 w ^ { 5 } s - 30 w ^ { 4 } s ^ { 2 } + 120 w ^ { 3 } s ^ { 3 } + 360 w ^ { 2 } s ^ { 4 } - 720 w s ^ { 5 } - 720 s ^ { 6 }$ 
A)  $w ^ { 6 } - 6 w ^ { 5 } s + 15 w ^ { 4 } s ^ { 2 } - 20 w ^ { 3 } s ^ { 3 } + 15 w ^ { 2 } s ^ { 4 } - 6 w s ^ { 5 } + s ^ { 6 }$ 
B)  $w ^ { 6 } - 8 w ^ { 5 } s + 17 w ^ { 4 } s ^ { 2 } - 22 w ^ { 3 } s ^ { 3 } + 17 w ^ { 2 } s ^ { 4 } - 8 w s ^ { 5 } + s ^ { 6 }$ 
C)  $w ^ { 6 } - s ^ { 6 }$ 
D)  $w ^ { 6 } - 6 w ^ { 5 } s - 30 w ^ { 4 } s ^ { 2 } + 120 w ^ { 3 } s ^ { 3 } + 360 w ^ { 2 } s ^ { 4 } - 720 w s ^ { 5 } - 720 s ^ { 6 }$

Question 13

Find the nth term of the geometric sequence.
-$$a = 2 ; r = - 4$$

Accepted Answer

A)  $a _ { n } = 2 \cdot 4 ^ { n - 1 }$ 
B)  $a _ { n } = - 4 \cdot 2 ^ { n - 1 }$ 
C)  $a _ { n } = 2 \cdot - 4 ^ { n }$ 
D)  $a _ { n } = 2 \cdot - 4 ^ { n - 1 }$ 
A)  $a _ { n } = 2 \cdot 4 ^ { n - 1 }$ 
B)  $a _ { n } = - 4 \cdot 2 ^ { n - 1 }$ 
C)  $a _ { n } = 2 \cdot - 4 ^ { n }$ 
D)  $a _ { n } = 2 \cdot - 4 ^ { n - 1 }$

Question 14

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of
summation.
-$$4 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + \frac { 15 } { 2 }$$

Accepted Answer

A)  $\sum _ { k = 8 } ^ { 15 } \frac { k } { 2 }$ 
B)  $\sum _ { \mathrm { k } = 8 } ^ { 12 } \frac { \mathrm { k } } { 2 }$ 
C)  $\sum _ { k = 1 } ^ { 15 } \frac { k } { 2 }$ 
D)  $\sum _ { k = 2 } ^ { 15 } \frac { k } { 2 }$ 
A)  $\sum _ { k = 8 } ^ { 15 } \frac { k } { 2 }$ 
B)  $\sum _ { \mathrm { k } = 8 } ^ { 12 } \frac { \mathrm { k } } { 2 }$ 
C)  $\sum _ { k = 1 } ^ { 15 } \frac { k } { 2 }$ 
D)  $\sum _ { k = 2 } ^ { 15 } \frac { k } { 2 }$

Question 15

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are
given.
-$$\begin{array} { l l } 
\mathrm { a } = - 2 ; & \mathrm { d } = 3 \
\mathrm { a } _ { \mathrm { n } } = ? ; & \mathrm { a } 7 = ?
\end{array}$$

Accepted Answer

A)  $a _ { n } = - 5 + 3 n ; a _ { 7 } = 16$ 
B)  $a _ { n } = - 5 + 3 n ; a 7 = 40$ 
C)  $a _ { n } = - 2 + 3 n ; a _ { 7 } = 16$ 
D)  $a _ { n } = - 5 - 3 n ; a 7 = 16$ 
A)  $a _ { n } = - 5 + 3 n ; a _ { 7 } = 16$ 
B)  $a _ { n } = - 5 + 3 n ; a 7 = 40$ 
C)  $a _ { n } = - 2 + 3 n ; a _ { 7 } = 16$ 
D)  $a _ { n } = - 5 - 3 n ; a 7 = 16$

Question 16

Find the sum of the sequence.
-$$\sum _ { k = 4 } ^ { 7 } 6 k$$

Accepted Answer

A)  132 
B)  90 
C)  42 
D)  66 
A)  132 
B)  90 
C)  42 
D)  66

Question 17

Find the sum of the sequence.
-$$\sum _ { k = 2 } ^ { 5 } ( - 1 ) ^ { k + 1 } ( k - 9 ) ^ { 2 }$$

Accepted Answer

A)  $- 1,914$ 
B)  126 
C)  $- 22$ 
D)  $- 126$ 
A)  $- 1,914$ 
B)  126 
C)  $- 22$ 
D)  $- 126$

Question 18

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.
-$$4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$$

Accepted Answer

First we show that the statement is true

Question 19

Solve the problem.
-A pendulum bob swings through an arc 60 inches long on its first swing. Each swing thereafter, it swings only 90% as far as on the previous swing. How far will it swing altogether before coming to a complete stop?

Accepted Answer

A)  67 inches 
B)  133 inches 
C)  300 inches 
D)  600 inches 
A)  67 inches 
B)  133 inches 
C)  300 inches 
D)  600 inches

Question 20

Choose the one alternative that best completes the statement or answers the question.
-The 5 th term in the expansion of $( 4 x + 2 y ) ^ { 9 }$

Accepted Answer

A)  $1,032,192 x ^ { 5 } y ^ { 5 }$ 
B)  $1,032,192 x ^ { 4 } y ^ { 5 }$ 
C)  $2,064,384 x ^ { 5 } y ^ { 4 }$ 
D)  $516,096 x ^ { 4 } y ^ { 5 }$ 
A)  $1,032,192 x ^ { 5 } y ^ { 5 }$ 
B)  $1,032,192 x ^ { 4 } y ^ { 5 }$ 
C)  $2,064,384 x ^ { 5 } y ^ { 4 }$ 
D)  $516,096 x ^ { 4 } y ^ { 5 }$

Write out the first five terms of the sequence. - $\left\{ \frac { ( 2 n - 1 ) ! } { n ! } \right\}$

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } 4 ( 3 ) ^ { \mathrm { k } }$

Express the sum using summation notation. - $2 ^ { 3 } + 3 ^ { 3 } + 4 ^ { 3 } + \cdots + 8 ^ { 3 }$

Write out the first five terms of the sequence. - $\left\{ \frac { n } { n ^ { 2 } + 2 } \right\}$

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - $0,2,6,12,20 , \ldots$

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. - $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 5 } ( \mathrm { k } + 1 )$

Express the sum using summation notation. - $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }$

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $\frac { 1 } { 5 } + \frac { 2 } { 5 } + \frac { 2 ^ { 2 } } { 5 } + \frac { 2 ^ { 3 } } { 5 } + \cdots + \frac { 2 ^ { 13 } } { 5 }$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - $\frac { 1 } { 7 } , \frac { 1 } { 9 } , \frac { 1 } { 11 } , \frac { 1 } { 13 }$

Expand the expression using the Binomial Theorem. - $( w - s ) ^ { 6 }$

Find the nth term of the geometric sequence. - $a = 2 ; r = - 4$

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of summation. - $4 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + \frac { 15 } { 2 }$

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. - =-2; =3 =?; 7=?

Find the sum of the sequence. - $\sum _ { k = 4 } ^ { 7 } 6 k$

Find the sum of the sequence. - $\sum _ { k = 2 } ^ { 5 } ( - 1 ) ^ { k + 1 } ( k - 9 ) ^ { 2 }$

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. - $4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$

Solve the problem. -A pendulum bob swings through an arc 60 inches long on its first swing. Each swing thereafter, it swings only 90% as far as on the previous swing. How far will it swing altogether before coming to a complete stop?

Choose the one alternative that best completes the statement or answers the question. -The 5 th term in the expansion of $( 4 x + 2 y ) ^ { 9 }$

Functions and Their Graphs

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Analytic Trigonometry

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Polar Coordinates; Vectors

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

Foundations: a Prelude to Functions

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Exam 11: Sequences; Induction; the Binomial Theorem

Write out the first five terms of the sequence. - {(2n−1)!n!}\left\{ \frac { ( 2 n - 1 ) ! } { n ! } \right\}{n!(2n−1)!​}

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - ∑k=154(3)k\sum _ { \mathrm { k } = 1 } ^ { 5 } 4 ( 3 ) ^ { \mathrm { k } }∑k=15​4(3)k

Express the sum using summation notation. - 23+33+43+⋯+832 ^ { 3 } + 3 ^ { 3 } + 4 ^ { 3 } + \cdots + 8 ^ { 3 }23+33+43+⋯+83

Write out the first five terms of the sequence. - {nn2+2}\left\{ \frac { n } { n ^ { 2 } + 2 } \right\}{n2+2n​}

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - 0,2,6,12,20,…0,2,6,12,20 , \ldots0,2,6,12,20,…

Find the sum of the sequence. - ∑k=15(k+1)\sum _ { k = 1 } ^ { 5 } ( \mathrm { k } + 1 )∑k=15​(k+1)

Express the sum using summation notation. - 45−1625+64125−⋯+(−1)(13+1)(45)13\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }54​−2516​+12564​−⋯+(−1)(13+1)(54​)13

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - 17,19,111,113\frac { 1 } { 7 } , \frac { 1 } { 9 } , \frac { 1 } { 11 } , \frac { 1 } { 13 }71​,91​,111​,131​

Expand the expression using the Binomial Theorem. - (w−s)6( w - s ) ^ { 6 }(w−s)6

Find the nth term of the geometric sequence. - a=2;r=−4a = 2 ; r = - 4a=2;r=−4

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of summation. - 4+92+5+112+…+1524 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + \frac { 15 } { 2 }4+29​+5+211​+…+215​