Question 1

Expand the expression using the Binomial Theorem.
-$$( 2 x + y ) ^ { 6 }$$

Accepted Answer

A)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 480 x ^ { 4 } y ^ { 2 } + 960 x ^ { 3 } y ^ { 3 } + 1440 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
B)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 60 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
C)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
D)  $2 x ^ { 6 } + 12 x ^ { 5 } y + 30 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
A)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 480 x ^ { 4 } y ^ { 2 } + 960 x ^ { 3 } y ^ { 3 } + 1440 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
B)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 60 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
C)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
D)  $2 x ^ { 6 } + 12 x ^ { 5 } y + 30 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 12 x y ^ { 5 } + y ^ { 6 }$

Question 2

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

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 3

Solve the problem.
-A theater has 20 rows with 23 seats in the first row, 27 in the second row, 31 in the third row, and so forth. How many seats are in the theater?

Accepted Answer

A)  1,260 seats 
B)  2,520 seats 
C)  2,440 seats 
D)  1,220 seats 
A)  1,260 seats 
B)  2,520 seats 
C)  2,440 seats 
D)  1,220 seats

Question 4

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 5

Determine whether the sequence is arithmetic.
--1, 1, 3, 5, 7, ...

Accepted Answer

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

Question 6

Find the nth term of the geometric sequence.
-$$a = 3 ; r = \left( \frac { 1 } { 3 } \right)$$

Accepted Answer

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

Question 7

Evaluate the expression.
-$$\left( \begin{array} { l } 
4 \
1
\end{array} \right)$$

Accepted Answer

A)  $\frac { 4 } { 3 }$ 
B)  4 
C)  1 
D)  4 ! 
A)  $\frac { 4 } { 3 }$ 
B)  4 
C)  1 
D)  4 !

Question 8

Find the sum of the arithmetic sequence.
--3 + 1 + 5 + 9 + 13 + ... + (4n - 7)

Accepted Answer

A)  n(2n - 5) 
B)  n(4n - 7) 
C)  n(4n + 7) 
D)  n(2n + 5) 
A)  n(2n - 5) 
B)  n(4n - 7) 
C)  n(4n + 7) 
D)  n(2n + 5)

Question 9

Find the indicated term using the given information.
-a = 3 , d = 3 ; a23

Accepted Answer

A)  69 
B)  72 
C)  -66 
D)  -63 
A)  69 
B)  72 
C)  -66 
D)  -63

Question 10

Express the repeating decimal as a fraction in lowest terms.
-$$0 . \overline { 4 } = \frac { 4 } { 10 } + \frac { 4 } { 100 } + \frac { 4 } { 1,000 } + \frac { 4 } { 10,000 } \ldots$$

Accepted Answer

A)  $\frac { 111 } { 250 }$ 
B)  $\frac { 4 } { 99 }$ 
C)  $\frac { 11 } { 25 }$ 
D)  $\frac { 4 } { 9 }$ 
A)  $\frac { 111 } { 250 }$ 
B)  $\frac { 4 } { 99 }$ 
C)  $\frac { 11 } { 25 }$ 
D)  $\frac { 4 } { 9 }$

Question 11

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
-Find $a _ { 12 } \text { when } a _ { 1 } = - 4 , r = 2$

Accepted Answer

A)  18 
B)  -8,192 
C)  -16,384 
D)  -8,188 
A)  18 
B)  -8,192 
C)  -16,384 
D)  -8,188

Question 12

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-24, 9.6, 3.84, 1.536, 0.61

Accepted Answer

A)  2.5 
B)  -0.4 
C)  0.4 
D)  0.61 
A)  2.5 
B)  -0.4 
C)  0.4 
D)  0.61

Question 13

Solve the problem.
-As Sunee improves her algebra skills, she takes 0.9 times as long to complete each homework assignment as she took to complete the preceeding assignment. If it took her 55 minutes to complete her first assignment, find
How long it took her to complete the fifth assignment. Find the total time she took to complete her first five
Homework assignments. (Round to the nearest minute.)

Accepted Answer

A)  32 min; 189 min 
B)  36 min; 225 min 
C)  32 min; 225 min 
D)  36 min; 189 min 
A)  32 min; 189 min 
B)  36 min; 225 min 
C)  32 min; 225 min 
D)  36 min; 189 min

Question 14

Evaluate the expression.
-$$\left( \begin{array} { l } 
9 \
9
\end{array} \right)$$

Accepted Answer

A)  1 
B)  362,880 
C)  0 
D)  2 
A)  1 
B)  362,880 
C)  0 
D)  2

Question 15

Evaluate the factorial expression.
-$\frac { 5 ! } { 3 ! }$

Accepted Answer

A)  2 ! 
B)  5 
C)  $\frac { 5 } { 2 }$ 
D)  20 
A)  2 ! 
B)  5 
C)  $\frac { 5 } { 2 }$ 
D)  20

Question 16

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

Question 17

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-$$\frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } + \frac { 1 } { 16 } + \ldots + \frac { 1 } { 2 ^ { n } } = 1 - \frac { 1 } { 2 ^ { n } }$$

Accepted Answer

When @#LAT-DLM&, the left side of the statement is

Question 18

Write the first four terms of the sequence whose general term is given.
-$\left\{ \frac { 3 ^ { n } } { ( n + 3 ) ! } \right\}$

Accepted Answer

A)  $\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 80 } , \frac { 9 } { 560 }$

В) $\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 40 } , \frac { 9 } { 280 }$ 
C)  $\frac { 3 } { 7 } , \frac { 9 } { 8 } , 3 , \frac { 81 } { 10 }$ 
D)  $\frac { 3 } { 4 } , \frac { 9 } { 5 } , \frac { 9 } { 2 } , \frac { 81 } { 7 }$ 
A)  $\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 80 } , \frac { 9 } { 560 }$

В) $\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 40 } , \frac { 9 } { 280 }$ 
C)  $\frac { 3 } { 7 } , \frac { 9 } { 8 } , 3 , \frac { 81 } { 10 }$ 
D)  $\frac { 3 } { 4 } , \frac { 9 } { 5 } , \frac { 9 } { 2 } , \frac { 81 } { 7 }$

Question 19

Find the sum.
-$$\sum _ { \mathrm { k } = 1 } ^ { 3 } \left( \frac { 2 } { 3 } \right) ^ { \mathrm { k } + 1 }$$

Accepted Answer

A)  $\frac { 38 } { 27 }$ 
B)  $\frac { 76 } { 81 }$ 
C)  $\frac { 260 } { 81 }$ 
D)  $\frac { 80 } { 81 }$ 
A)  $\frac { 38 } { 27 }$ 
B)  $\frac { 76 } { 81 }$ 
C)  $\frac { 260 } { 81 }$ 
D)  $\frac { 80 } { 81 }$

Question 20

Evaluate the factorial expression.
-$\frac { 2 ! } { 4 ! }$

Accepted Answer

A)  12 
B)  $\frac { 1 } { 2 ! }$ 
C)  $\frac { 1 } { 12 }$ 
D)  2 ! 
A)  12 
B)  $\frac { 1 } { 2 ! }$ 
C)  $\frac { 1 } { 12 }$ 
D)  2 !

Expand the expression using the Binomial Theorem. - $( 2 x + y ) ^ { 6 }$

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. - a=-2; d=3 =?; a7=?

Solve the problem. -A theater has 20 rows with 23 seats in the first row, 27 in the second row, 31 in the third row, and so forth. How many seats are in the theater?

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

Determine whether the sequence is arithmetic. --1, 1, 3, 5, 7, ...

Find the nth term of the geometric sequence. - $a = 3 ; r = \left( \frac { 1 } { 3 } \right)$

Evaluate the expression. - $\left( \begin{array} { l } 4 \\1\end{array} \right)$

Find the sum of the arithmetic sequence. --3 + 1 + 5 + 9 + 13 + ... + (4n - 7)

Find the indicated term using the given information. -a = 3 , d = 3 ; a23

Express the repeating decimal as a fraction in lowest terms. - $0 . \overline { 4 } = \frac { 4 } { 10 } + \frac { 4 } { 100 } + \frac { 4 } { 1,000 } + \frac { 4 } { 10,000 } \ldots$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find $a _ { 12 } \text { when } a _ { 1 } = - 4 , r = 2$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. -24, 9.6, 3.84, 1.536, 0.61

Evaluate the expression. - $\left( \begin{array} { l } 9 \\9\end{array} \right)$

Evaluate the factorial expression. - $\frac { 5 ! } { 3 ! }$

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 the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. - $\frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } + \frac { 1 } { 16 } + \ldots + \frac { 1 } { 2 ^ { n } } = 1 - \frac { 1 } { 2 ^ { n } }$

Write the first four terms of the sequence whose general term is given. - $\left\{ \frac { 3 ^ { n } } { ( n + 3 ) ! } \right\}$

Find the sum. - $\sum _ { \mathrm { k } = 1 } ^ { 3 } \left( \frac { 2 } { 3 } \right) ^ { \mathrm { k } + 1 }$

Evaluate the factorial expression. - $\frac { 2 ! } { 4 ! }$

Functions and Their Graphs

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Analytic Trigonometry

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Exam 11: Sequences; Induction; the Binomial Theorem

Expand the expression using the Binomial Theorem. - (2x+y)6( 2 x + y ) ^ { 6 }(2x+y)6