Question 1

Write the first five terms of the sequence. (Assume that $n$ begins with 1.)
$$a _ { n } = ( - 1 ) ^ { n } ( n - 1 ) ( n - 2 )$$

Accepted Answer

A)  $4,0,0 , - 2,6$ 
B)  $0,0 , - 2,6 , - 12$ 
C)  $0,0 , - 2 , - 6 , - 12$ 
D)  $0,2 , - 6,12 , - 20$ 
E)  $0 , - 1,2 , - 3,4$ 
A)  $4,0,0 , - 2,6$ 
B)  $0,0 , - 2,6 , - 12$ 
C)  $0,0 , - 2 , - 6 , - 12$ 
D)  $0,2 , - 6,12 , - 20$ 
E)  $0 , - 1,2 , - 3,4$

Question 2

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that $n$ begins with 1 .)
$$a _ { n } = 6 + 4 n$$

Accepted Answer

A)  $- 4$ 
B)  $- 6$ 
C)  6 
D)  4 
E)  not arithmetic 
A)  $- 4$ 
B)  $- 6$ 
C)  6 
D)  4 
E)  not arithmetic

Question 3

Find the sum of the infinite series.
$$\sum _ { i = 1 } ^ { \infty } 3 \left( \frac { 1 } { 3 } \right) ^ { i }$$

Accepted Answer

A)  undefined 
B)  $\frac { 3 } { 4 }$ 
C)  3 
D)  $\frac { 9 } { 4 }$ 
E)  $\frac { 3 } { 2 }$ 
A)  undefined 
B)  $\frac { 3 } { 4 }$ 
C)  3 
D)  $\frac { 9 } { 4 }$ 
E)  $\frac { 3 } { 2 }$

Question 4

Calculate the binomial coefficient: $\left( \begin{array} { l } 8 \ 7 \end{array} \right)$

Accepted Answer

A)  40,320 
B)  56 
C)  8 
D)  1 
E)  0 
A)  40,320 
B)  56 
C)  8 
D)  1 
E)  0

Question 5

Use sigma notation to write the sum.
$$\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \cdots + \frac { 1 } { 9 \cdot 8 }$$

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 7 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
B)  $\sum _ { n = 1 } ^ { 7 } \frac { 1 } { n ( n + 1 ) }$ 
C)  $\sum _ { n = 1 } ^ { 7 } \frac { n } { ( n + 2 ) ! }$ 
D)  $\sum _ { n = 1 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
E)  $\sum _ { n = 0 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
A)  $\sum _ { n = 1 } ^ { 7 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
B)  $\sum _ { n = 1 } ^ { 7 } \frac { 1 } { n ( n + 1 ) }$ 
C)  $\sum _ { n = 1 } ^ { 7 } \frac { n } { ( n + 2 ) ! }$ 
D)  $\sum _ { n = 1 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
E)  $\sum _ { n = 0 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$

Question 6

Find the indicated sum.
$\sum _ { n = 1 } ^ { 8 } n ^ { 4 }$

Accepted Answer

A)  4096 
B)  $1,679,616$ 
C)  36 
D)  87,380 
E)  8772 
A)  4096 
B)  $1,679,616$ 
C)  36 
D)  87,380 
E)  8772

Question 7

Determine whether the sequence is geometric. If so, find the common ratio. $- 2 , - 6 , - 18 , - 54 , \ldots$

Accepted Answer

A)  3 
B)  $- 2$ 
C)  $\frac { 1 } { 3 }$ 
D)  $- 3$ 
E)  not geometric 
A)  3 
B)  $- 2$ 
C)  $\frac { 1 } { 3 }$ 
D)  $- 3$ 
E)  not geometric

Question 8

Determine whether the sequence is geometric. If so, find the common ratio. $- 1 , - 2 , - 4 , - 8 , \ldots$

Accepted Answer

A)  2 
B)  $- 1$ 
C)  $\frac { 1 } { 2 }$ 
D)  $- 2$ 
E)  not geometric 
A)  2 
B)  $- 1$ 
C)  $\frac { 1 } { 2 }$ 
D)  $- 2$ 
E)  not geometric

Question 9

Find the sum of the finite geometric sequence.
$$\sum _ { n = 1 } ^ { 6 } 2 \left( - \frac { 2 } { 3 } \right) ^ { n - 1 }$$

Accepted Answer

A)  $- \frac { 463 } { 243 }$ 
B)  $- \frac { 1024 } { 3 }$ 
C)  4256 
D)  $\frac { 55 } { 81 }$ 
E)  $\frac { 266 } { 243 }$ 
A)  $- \frac { 463 } { 243 }$ 
B)  $- \frac { 1024 } { 3 }$ 
C)  4256 
D)  $\frac { 55 } { 81 }$ 
E)  $\frac { 266 } { 243 }$

Question 10

Determine the number of ways a computer can randomly generate a prime integer between 10 and 20 .

Accepted Answer

A)  4 
B)  3 
C)  2 
D)  5 
E)  11 
A)  4 
B)  3 
C)  2 
D)  5 
E)  11

Question 11

Find $P _ { k + 1 }$ for the given $P _ { k }$.
$$P _ { k } = \frac { 4 } { k ( k + 1 ) }$$

Accepted Answer

A)  $P _ { k + 1 } = \frac { 4 } { k ( k + 1 ) } + 1$ 
B)  $P _ { k + 1 } = \frac { 4 } { k ( k + 1 ) } + \frac { 4 } { ( k + 1 ) ( k + 2 ) }$ 
C)  $P _ { k + 1 } = \frac { 4 } { ( k + 1 ) ( k + 2 ) }$ 
D)  $P _ { k + 1 } = \frac { 4 } { k ( k + 2 ) }$ 
E)  $\quad P _ { k + 1 } = \frac { 16 } { ( k + 1 ) ( k + 2 ) }$ 
A)  $P _ { k + 1 } = \frac { 4 } { k ( k + 1 ) } + 1$ 
B)  $P _ { k + 1 } = \frac { 4 } { k ( k + 1 ) } + \frac { 4 } { ( k + 1 ) ( k + 2 ) }$ 
C)  $P _ { k + 1 } = \frac { 4 } { ( k + 1 ) ( k + 2 ) }$ 
D)  $P _ { k + 1 } = \frac { 4 } { k ( k + 2 ) }$ 
E)  $\quad P _ { k + 1 } = \frac { 16 } { ( k + 1 ) ( k + 2 ) }$

Question 12

Determine the sample space for the experiment.
Two marbles are selected from marbles labeled A through $\mathrm { E }$ where the marbles are not replaced and the order of selection does not matter.

Accepted Answer

A)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } \}$ 
B)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } \}$ 
C)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { DE } \}$ 
D)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } , \mathrm { DA } , \mathrm { DB } \}$ 
E)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CA } , \mathrm { CB } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } \}$ 
A)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } \}$ 
B)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } \}$ 
C)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { DE } \}$ 
D)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } , \mathrm { DA } , \mathrm { DB } \}$ 
E)  $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CA } , \mathrm { CB } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } \}$

Question 13

Find the rational number representation of the repeating decimal.
$0 . \overline { 157 }$

Accepted Answer

A)  $\frac { 157 } { 9999 }$ 
B)  $\frac { 15.7 } { 999 }$ 
C)  $\frac { 157 } { 9 }$ 
D)  $\frac { 157 } { 999 }$ 
E)  $\frac { 157 } { 99 }$ 
A)  $\frac { 157 } { 9999 }$ 
B)  $\frac { 15.7 } { 999 }$ 
C)  $\frac { 157 } { 9 }$ 
D)  $\frac { 157 } { 999 }$ 
E)  $\frac { 157 } { 99 }$

Question 14

Write the first five terms of the geometric sequence.
$$a _ { 1 } = 4 , r = - \frac { 1 } { 5 }$$

Accepted Answer

A)  $4 , - 1 , - 6 , - 11 , - 16$ 
B)  $4 , - 20,100 , - 500,2500$ 
C)  $- \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 } , \frac { 4 } { 625 } , - \frac { 4 } { 3125 }$ 
D)  $1,4 , - \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 }$ 
E)  $4 , - \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 } , \frac { 4 } { 625 }$ 
A)  $4 , - 1 , - 6 , - 11 , - 16$ 
B)  $4 , - 20,100 , - 500,2500$ 
C)  $- \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 } , \frac { 4 } { 625 } , - \frac { 4 } { 3125 }$ 
D)  $1,4 , - \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 }$ 
E)  $4 , - \frac { 4 } { 5 } , \frac { 4 } { 25 } , - \frac { 4 } { 125 } , \frac { 4 } { 625 }$

Question 15

Determine whether the sequence is arithmetic. If so, find the common difference. $- 3 , - 7 , - 11 , - 15 , - 19$

Accepted Answer

A)  1 
B)  $- 4$ 
C)  $- 3$ 
D)  4 
E)  not arithmetic 
A)  1 
B)  $- 4$ 
C)  $- 3$ 
D)  4 
E)  not arithmetic

Question 16

Find a formula for $a _ { n }$ for the arithmetic sequence.
$$a _ { 4 } = - 13 , a _ { 13 } = - 31$$

Accepted Answer

A)  $a _ { n } = - 7 - 2 n$ 
B)  $a _ { n } = 5 - 7 n$ 
C)  $a _ { n } = - 2 - 7 n$ 
D)  $a _ { n } = - 7 ( - 2 ) ^ { n }$ 
E)  $a _ { n } = - 5 - 2 n$ 
A)  $a _ { n } = - 7 - 2 n$ 
B)  $a _ { n } = 5 - 7 n$ 
C)  $a _ { n } = - 2 - 7 n$ 
D)  $a _ { n } = - 7 ( - 2 ) ^ { n }$ 
E)  $a _ { n } = - 5 - 2 n$

Question 17

Use the Binomial Theorem to expand and simplify the expression.
$$\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$$

Accepted Answer

A)  $x ^ { 3 } + 625$ 
B)  $x ^ { 12 } - 20 x ^ { 9 } + 150 x ^ { 6 } - 500 x ^ { 3 } + 625$ 
C)  $x ^ { 3 } - 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } - 500 x ^ { 3 / 4 } + 625$ 
D)  $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$ 
E)  $x ^ { 12 } + 20 x ^ { 9 } + 150 x ^ { 6 } + 500 x ^ { 3 } + 625$ 
A)  $x ^ { 3 } + 625$ 
B)  $x ^ { 12 } - 20 x ^ { 9 } + 150 x ^ { 6 } - 500 x ^ { 3 } + 625$ 
C)  $x ^ { 3 } - 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } - 500 x ^ { 3 / 4 } + 625$ 
D)  $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$ 
E)  $x ^ { 12 } + 20 x ^ { 9 } + 150 x ^ { 6 } + 500 x ^ { 3 } + 625$

Question 18

Determine the sample space for the experiment.
Four coins are flipped and the number of heads observed is recorded.

Accepted Answer

A)  $S = \{ 1,2,3,4 \}$ 
B)  $S = \{ 4 \}$ 
C)  $S = \{ 0,1,2,3,4 \}$ 
D)  $S = \{ \mathrm { HT } , \mathrm { TH } \}$ 
E)  $S = \{ \mathrm { HHHH } \}$ 
A)  $S = \{ 1,2,3,4 \}$ 
B)  $S = \{ 4 \}$ 
C)  $S = \{ 0,1,2,3,4 \}$ 
D)  $S = \{ \mathrm { HT } , \mathrm { TH } \}$ 
E)  $S = \{ \mathrm { HHHH } \}$

Question 19

Find the indicated $n$th term of the geometric sequence.
5 th term: $a _ { 3 } = - \frac { 3 } { 16 } , a _ { 9 } = - \frac { 3 } { 65,536 }$

Accepted Answer

A)  $\frac { 3 } { 1024 }$ 
B)  $- \frac { 4 } { 81 }$ 
C)  $- \frac { 3 } { 4096 }$ 
D)  $- \frac { 3 } { 256 }$ 
E)  $\frac { 3 } { 64 }$ 
A)  $\frac { 3 } { 1024 }$ 
B)  $- \frac { 4 } { 81 }$ 
C)  $- \frac { 3 } { 4096 }$ 
D)  $- \frac { 3 } { 256 }$ 
E)  $\frac { 3 } { 64 }$

Question 20

Write the first five terms of the arithmetic sequence.
$$a _ { 5 } = - 29 , a _ { 10 } = - 59$$

Accepted Answer

A)  $- 5,1,7,13,19$ 
B)  $- 11 , - 17 , - 23 , - 29 , - 35$ 
C)  $- 5 , - 11 , - 17 , - 23 , - 29$ 
D)  $- 5,30 , - 180,1080 , - 6480$ 
E)  $- 5 , - 11 , - 16 , - 21 , - 26$ 
A)  $- 5,1,7,13,19$ 
B)  $- 11 , - 17 , - 23 , - 29 , - 35$ 
C)  $- 5 , - 11 , - 17 , - 23 , - 29$ 
D)  $- 5,30 , - 180,1080 , - 6480$ 
E)  $- 5 , - 11 , - 16 , - 21 , - 26$

Write the first five terms of the sequence. (Assume that $n$ begins with 1.) $a _ { n } = ( - 1 ) ^ { n } ( n - 1 ) ( n - 2 )$

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that $n$ begins with 1 .) $a _ { n } = 6 + 4 n$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 3 \left( \frac { 1 } { 3 } \right) ^ { i }$

Calculate the binomial coefficient: $\left( \begin{array} { l } 8 \\ 7 \end{array} \right)$

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \cdots + \frac { 1 } { 9 \cdot 8 }$

Find the indicated sum. $\sum _ { n = 1 } ^ { 8 } n ^ { 4 }$

Determine whether the sequence is geometric. If so, find the common ratio. $- 2 , - 6 , - 18 , - 54 , \ldots$

Determine whether the sequence is geometric. If so, find the common ratio. $- 1 , - 2 , - 4 , - 8 , \ldots$

Find the sum of the finite geometric sequence. $\sum _ { n = 1 } ^ { 6 } 2 \left( - \frac { 2 } { 3 } \right) ^ { n - 1 }$

Determine the number of ways a computer can randomly generate a prime integer between 10 and 20 .

Find $P _ { k + 1 }$ for the given $P _ { k }$ . $P _ { k } = \frac { 4 } { k ( k + 1 ) }$

Determine the sample space for the experiment. Two marbles are selected from marbles labeled A through $\mathrm { E }$ where the marbles are not replaced and the order of selection does not matter.

Find the rational number representation of the repeating decimal. $0 . \overline { 157 }$

Write the first five terms of the geometric sequence. $a _ { 1 } = 4 , r = - \frac { 1 } { 5 }$

Determine whether the sequence is arithmetic. If so, find the common difference. $- 3 , - 7 , - 11 , - 15 , - 19$

Find a formula for $a _ { n }$ for the arithmetic sequence. $a _ { 4 } = - 13 , a _ { 13 } = - 31$

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$

Determine the sample space for the experiment. Four coins are flipped and the number of heads observed is recorded.

Find the indicated $n$ th term of the geometric sequence. 5 th term: $a _ { 3 } = - \frac { 3 } { 16 } , a _ { 9 } = - \frac { 3 } { 65,536 }$

Write the first five terms of the arithmetic sequence. $a _ { 5 } = - 29 , a _ { 10 } = - 59$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

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Exam 8: Sequences, Series, and Probability

Write the first five terms of the sequence. (Assume that nnn begins with 1.) an=(−1)n(n−1)(n−2)a _ { n } = ( - 1 ) ^ { n } ( n - 1 ) ( n - 2 )an​=(−1)n(n−1)(n−2)

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that nnn begins with 1 .) an=6+4na _ { n } = 6 + 4 nan​=6+4n

Find the sum of the infinite series. ∑i=1∞3(13)i\sum _ { i = 1 } ^ { \infty } 3 \left( \frac { 1 } { 3 } \right) ^ { i }∑i=1∞​3(31​)i

Calculate the binomial coefficient: (87)\left( \begin{array} { l } 8 \\ 7 \end{array} \right)(87​)

Use sigma notation to write the sum. 13⋅2+14⋅3+⋯+19⋅8\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \cdots + \frac { 1 } { 9 \cdot 8 }3⋅21​+4⋅31​+⋯+9⋅81​

Find the indicated sum. ∑n=18n4\sum _ { n = 1 } ^ { 8 } n ^ { 4 }∑n=18​n4

Determine whether the sequence is geometric. If so, find the common ratio. −2,−6,−18,−54,…- 2 , - 6 , - 18 , - 54 , \ldots−2,−6,−18,−54,…

Determine whether the sequence is geometric. If so, find the common ratio. −1,−2,−4,−8,…- 1 , - 2 , - 4 , - 8 , \ldots−1,−2,−4,−8,…

Find the sum of the finite geometric sequence. ∑n=162(−23)n−1\sum _ { n = 1 } ^ { 6 } 2 \left( - \frac { 2 } { 3 } \right) ^ { n - 1 }∑n=16​2(−32​)n−1

Determine the number of ways a computer can randomly generate a prime integer between 10 and 20 .

Find Pk+1P _ { k + 1 }Pk+1​ for the given PkP _ { k }Pk​ . Pk=4k(k+1)P _ { k } = \frac { 4 } { k ( k + 1 ) }Pk​=k(k+1)4​

Determine the sample space for the experiment. Two marbles are selected from marbles labeled A through E\mathrm { E }E where the marbles are not replaced and the order of selection does not matter.

Find the rational number representation of the repeating decimal. 0.157‾0 . \overline { 157 }0.157

Write the first five terms of the geometric sequence. a1=4,r=−15a _ { 1 } = 4 , r = - \frac { 1 } { 5 }a1​=4,r=−51​

Determine whether the sequence is arithmetic. If so, find the common difference. −3,−7,−11,−15,−19- 3 , - 7 , - 11 , - 15 , - 19−3,−7,−11,−15,−19

Find a formula for ana _ { n }an​ for the arithmetic sequence. a4=−13,a13=−31a _ { 4 } = - 13 , a _ { 13 } = - 31a4​=−13,a13​=−31

Use the Binomial Theorem to expand and simplify the expression. (x3/4−5)4\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }(x3/4−5)4

Determine the sample space for the experiment. Four coins are flipped and the number of heads observed is recorded.

Find the indicated nnn th term of the geometric sequence. 5 th term: a3=−316,a9=−365,536a _ { 3 } = - \frac { 3 } { 16 } , a _ { 9 } = - \frac { 3 } { 65,536 }a3​=−163​,a9​=−65,5363​

Write the first five terms of the arithmetic sequence. a5=−29,a10=−59a _ { 5 } = - 29 , a _ { 10 } = - 59a5​=−29,a10​=−59

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Write the first five terms of the sequence. (Assume that $n$ begins with 1.) $a _ { n } = ( - 1 ) ^ { n } ( n - 1 ) ( n - 2 )$

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that $n$ begins with 1 .) $a _ { n } = 6 + 4 n$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 3 \left( \frac { 1 } { 3 } \right) ^ { i }$

Calculate the binomial coefficient: $\left( \begin{array} { l } 8 \\ 7 \end{array} \right)$

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \cdots + \frac { 1 } { 9 \cdot 8 }$

Find the indicated sum. $\sum _ { n = 1 } ^ { 8 } n ^ { 4 }$

Determine whether the sequence is geometric. If so, find the common ratio. $- 2 , - 6 , - 18 , - 54 , \ldots$

Determine whether the sequence is geometric. If so, find the common ratio. $- 1 , - 2 , - 4 , - 8 , \ldots$

Find the sum of the finite geometric sequence. $\sum _ { n = 1 } ^ { 6 } 2 \left( - \frac { 2 } { 3 } \right) ^ { n - 1 }$

Find $P _ { k + 1 }$ for the given $P _ { k }$ . $P _ { k } = \frac { 4 } { k ( k + 1 ) }$

Determine the sample space for the experiment. Two marbles are selected from marbles labeled A through $\mathrm { E }$ where the marbles are not replaced and the order of selection does not matter.

Find the rational number representation of the repeating decimal. $0 . \overline { 157 }$

Write the first five terms of the geometric sequence. $a _ { 1 } = 4 , r = - \frac { 1 } { 5 }$

Determine whether the sequence is arithmetic. If so, find the common difference. $- 3 , - 7 , - 11 , - 15 , - 19$

Find a formula for $a _ { n }$ for the arithmetic sequence. $a _ { 4 } = - 13 , a _ { 13 } = - 31$

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$

Find the indicated $n$ th term of the geometric sequence. 5 th term: $a _ { 3 } = - \frac { 3 } { 16 } , a _ { 9 } = - \frac { 3 } { 65,536 }$

Write the first five terms of the arithmetic sequence. $a _ { 5 } = - 29 , a _ { 10 } = - 59$