Question 1

Find the sum of the infinite geometric series.
-$- 12 - 3 - \frac { 3 } { 4 } - \frac { 3 } { 16 } - \ldots$ . . .

Accepted Answer

A) - 16 
B)  $- \frac { 63 } { 4 }$ 
C) -12 
D) 4 
A) - 16 
B)  $- \frac { 63 } { 4 }$ 
C) -12 
D) 4

Question 2

Find the sum of the terms in the geometric sequence.
-$- 10 , - 5 , - \frac { 5 } { 2 } , - \frac { 5 } { 4 } , \ldots$

Accepted Answer

A)  $- \frac { 35 } { 2 }$ 
B) -10 
C) 10 
D) - 20 
A)  $- \frac { 35 } { 2 }$ 
B) -10 
C) 10 
D) - 20

Question 3

Find the indicated quantity of the arithmetic sequence.
-a1 = -19, d = -3; find $\mathrm { a } _ { 120 }$ 120

Accepted Answer

A) -376 
B) 338 
C) -379 
D) 341 
A) -376 
B) 338 
C) -379 
D) 341

Question 4

Find the indicated term of the geometric sequence.
-a1 = 9, r = -3; find $a _ { 5 }$

Accepted Answer

A) 81 
B) 729 
C) -729 
D) -2187 
A) 81 
B) 729 
C) -729 
D) -2187

Question 5

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.
-Find the sum of the odd integers between 18 and 54.

Accepted Answer

A) 684 
B) 720 
C) 648 
D) 612 
A) 684 
B) 720 
C) 648 
D) 612

Question 6

Determine the first five terms of the geometric sequence.
-$a _ { 1 } = - 2 , r = - 3$

Accepted Answer

A) -2, 6, -18, 54, -162 
B) -3, 6, -18, 54, -162 
C) -2, -6, -18, 54, -162 
D) -2, -5, -8, -11, -14 
A) -2, 6, -18, 54, -162 
B) -3, 6, -18, 54, -162 
C) -2, -6, -18, 54, -162 
D) -2, -5, -8, -11, -14

Question 7

Find the sum of the infinite geometric series.
-$4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \frac { 4 } { 125 } + \ldots$

Accepted Answer

A)  $\frac { 4 } { 5 }$ 
B)  $\frac { 24 } { 5 }$ 
C) 5 
D) 4 
A)  $\frac { 4 } { 5 }$ 
B)  $\frac { 24 } { 5 }$ 
C) 5 
D) 4

Question 8

Find the indicated term of the geometric sequence.
-a1 = 6, r = -2; find $a _ { 11 }$

Accepted Answer

A) 6148 
B) -14 
C) -12,288 
D) 6144 
A) 6148 
B) -14 
C) -12,288 
D) 6144

Question 9

Evaluate the combination.
-$\left( \begin{array} { l } 
5 \
2
\end{array} \right)$

Accepted Answer

A) 5 
B) 1 
C) 0 
D) 10 
A) 5 
B) 1 
C) 0 
D) 10

Question 10

Solve the problem.
-A song is selected at random from a jukebox containing 40 rock/pop songs, 15 country songs, and 6 classical pieces.
Find the probability: P(selecting a rock/pop song or a country song)

Accepted Answer

A) 118 
B) 5561 
C) 612 
D) 551 
A) 118 
B) 5561 
C) 612 
D) 551

Question 11

Write the first five terms of the arithmetic sequence with the given term and common difference.
-$\mathrm { a } _ { 1 } = 1.4 , \mathrm {~d} = 0.7$

Accepted Answer

A)  $2.1,2.8,3.5,4.2,4.9$ 
B)  $1.4,0.7,0 , - 0.7 , - 1.4$ 
C)  $0.7,0 , - 0.7 , - 1.4 , - 2.1$ 
D)  $1.4,2.1,2.8,3.5,4.2$ 
A)  $2.1,2.8,3.5,4.2,4.9$ 
B)  $1.4,0.7,0 , - 0.7 , - 1.4$ 
C)  $0.7,0 , - 0.7 , - 1.4 , - 2.1$ 
D)  $1.4,2.1,2.8,3.5,4.2$

Question 12

Use the binomial theorem to expand the expression.
-$( 3 x - 5 y ) ^ { 3 }$

Accepted Answer

A)  $9 x ^ { 3 } y - 15 x ^ { 2 } y ^ { 2 } + 25 x y ^ { 3 }$ 
B)  $27 x ^ { 3 } - 135 x ^ { 2 } y + 225 x y ^ { 2 } - 125 y ^ { 3 }$ 
C)  $27 x ^ { 3 } - 45 x ^ { 2 } y + 75 x y ^ { 2 } - 125 y ^ { 3 }$ 
D)  $9 x ^ { 3 } y - 30 x ^ { 2 } y ^ { 2 } + 25 x y ^ { 3 }$ 
A)  $9 x ^ { 3 } y - 15 x ^ { 2 } y ^ { 2 } + 25 x y ^ { 3 }$ 
B)  $27 x ^ { 3 } - 135 x ^ { 2 } y + 225 x y ^ { 2 } - 125 y ^ { 3 }$ 
C)  $27 x ^ { 3 } - 45 x ^ { 2 } y + 75 x y ^ { 2 } - 125 y ^ { 3 }$ 
D)  $9 x ^ { 3 } y - 30 x ^ { 2 } y ^ { 2 } + 25 x y ^ { 3 }$

Question 13

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
-$\frac { 1 } { 4 } , \frac { 3 } { 4 } , \frac { 9 } { 4 } , \frac { 27 } { 4 } , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 4 } ( 3 ) ^ { n - 1 }$ 
B)  $a _ { n } = \left( \frac { 1 } { 4 } \right) ^ { n - 1 } + \frac { 1 } { 2 }$ 
C)  $a _ { n } = \frac { 1 } { 4 } + \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = \frac { 1 } { 4 } + 3 ( n - 1 )$ 
A)  $a _ { n } = \frac { 1 } { 4 } ( 3 ) ^ { n - 1 }$ 
B)  $a _ { n } = \left( \frac { 1 } { 4 } \right) ^ { n - 1 } + \frac { 1 } { 2 }$ 
C)  $a _ { n } = \frac { 1 } { 4 } + \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = \frac { 1 } { 4 } + 3 ( n - 1 )$

Question 14

Write the first five terms of the arithmetic sequence with the given term and common difference.
-$a _ { 1 } = - 24 , d = 6$

Accepted Answer

A) -24, -18, -12, -6, 0 
B) 0, -6, -12, -18, -24 
C) -12, -18, -24, -30, -36 
D) -12, -6, 0, 6, 12 
A) -24, -18, -12, -6, 0 
B) 0, -6, -12, -18, -24 
C) -12, -18, -24, -30, -36 
D) -12, -6, 0, 6, 12

Question 15

Evaluate the expression.
-${ } _ { 9 } C _ { 1 }$

Accepted Answer

A) 362,880 
B) 1 
C) 8 
D) 9 
A) 362,880 
B) 1 
C) 8 
D) 9

Question 16

Write the first five terms of the sequence whose nth term is shown.
-$a _ { n } = n - 6$

Accepted Answer

A) -24, -18, -12, -6, 0 
B) 1, 2, 3, 4, 5 
C) -6, -5, -4, -3, -2 
D) -5, -4, -3, -2, -1 
A) -24, -18, -12, -6, 0 
B) 1, 2, 3, 4, 5 
C) -6, -5, -4, -3, -2 
D) -5, -4, -3, -2, -1

Question 17

Solve the problem.
-A bouncy ball is dropped from a height of 9 ft and always reboundsand always rebounds $\frac { 1 } { 3 }$ of the of the distance fallen. Find the total sum of the rebound heights of the ball.

Accepted Answer

A) 6 ft 
B) 3 ft 
C) 4.5 ft 
D) 13.5 ft 
A) 6 ft 
B) 3 ft 
C) 4.5 ft 
D) 13.5 ft

Question 18

Find the indicated quantity of the arithmetic sequence.
-a1 = 7 , d = 1 ; find $\mathrm { a } _ { 13 }$

Accepted Answer

A) - 6 
B) - 5 
C) 20 
D) 19 
A) - 6 
B) - 5 
C) 20 
D) 19

Question 19

Find the indicated sum.
-$a _ { 1 } = 4 , r = 2 ; \text { find } s 8$

Accepted Answer

A) 1022 
B) 1057 
C) 1000 
D) 1020 
A) 1022 
B) 1057 
C) 1000 
D) 1020

Question 20

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.
-$a _ { 1 } = - 2 , d = 0.2$

Accepted Answer

A)  $a _ { n } = - 2 n + 2.2$ 
B)  $a _ { n } = 0.2 n - 2$ 
C)  $a _ { n } = 0.2 n - 2.2$ 
D)  $a _ { n } = - 2 n + 0.2$ 
A)  $a _ { n } = - 2 n + 2.2$ 
B)  $a _ { n } = 0.2 n - 2$ 
C)  $a _ { n } = 0.2 n - 2.2$ 
D)  $a _ { n } = - 2 n + 0.2$

Find the sum of the infinite geometric series. - $- 12 - 3 - \frac { 3 } { 4 } - \frac { 3 } { 16 } - \ldots$ . . .

Find the sum of the terms in the geometric sequence. - $- 10 , - 5 , - \frac { 5 } { 2 } , - \frac { 5 } { 4 } , \ldots$

Find the indicated quantity of the arithmetic sequence. -a1 = -19, d = -3; find $\mathrm { a } _ { 120 }$ 120

Find the indicated term of the geometric sequence. -a1 = 9, r = -3; find $a _ { 5 }$

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. -Find the sum of the odd integers between 18 and 54.

Determine the first five terms of the geometric sequence. - $a _ { 1 } = - 2 , r = - 3$

Find the sum of the infinite geometric series. - $4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \frac { 4 } { 125 } + \ldots$

Find the indicated term of the geometric sequence. -a1 = 6, r = -2; find $a _ { 11 }$

Evaluate the combination. - $\left( \begin{array} { l } 5 \\2\end{array} \right)$

Solve the problem. -A song is selected at random from a jukebox containing 40 rock/pop songs, 15 country songs, and 6 classical pieces. Find the probability: P(selecting a rock/pop song or a country song)

Write the first five terms of the arithmetic sequence with the given term and common difference. - $\mathrm { a } _ { 1 } = 1.4 , \mathrm {~d} = 0.7$

Use the binomial theorem to expand the expression. - $( 3 x - 5 y ) ^ { 3 }$

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence. - $\frac { 1 } { 4 } , \frac { 3 } { 4 } , \frac { 9 } { 4 } , \frac { 27 } { 4 } , \ldots$

Write the first five terms of the arithmetic sequence with the given term and common difference. - $a _ { 1 } = - 24 , d = 6$

Evaluate the expression. - ${ } _ { 9 } C _ { 1 }$

Write the first five terms of the sequence whose nth term is shown. - $a _ { n } = n - 6$

Solve the problem. -A bouncy ball is dropped from a height of 9 ft and always reboundsand always rebounds $\frac { 1 } { 3 }$ of the of the distance fallen. Find the total sum of the rebound heights of the ball.

Find the indicated quantity of the arithmetic sequence. -a1 = 7 , d = 1 ; find $\mathrm { a } _ { 13 }$

Find the indicated sum. - $a _ { 1 } = 4 , r = 2 ; \text { find } s 8$

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence. - $a _ { 1 } = - 2 , d = 0.2$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Filters

Exam 12: Sequences, Series, and Probability

Find the sum of the infinite geometric series. - −12−3−34−316−…- 12 - 3 - \frac { 3 } { 4 } - \frac { 3 } { 16 } - \ldots−12−3−43​−163​−… . . .

Find the sum of the terms in the geometric sequence. - −10,−5,−52,−54,…- 10 , - 5 , - \frac { 5 } { 2 } , - \frac { 5 } { 4 } , \ldots−10,−5,−25​,−45​,…

Find the indicated quantity of the arithmetic sequence. -a1 = -19, d = -3; find a120\mathrm { a } _ { 120 }a120​ 120

Find the indicated term of the geometric sequence. -a1 = 9, r = -3; find a5a _ { 5 }a5​

Find the sum,m, sn,\mathrm { s } _ { \mathbf { n } },sn​, , o f the sequence. -Find the sum of the odd integers between 18 and 54.

Determine the first five terms of the geometric sequence. - a1=−2,r=−3a _ { 1 } = - 2 , r = - 3a1​=−2,r=−3

Find the sum of the infinite geometric series. - 4+45+425+4125+…4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \frac { 4 } { 125 } + \ldots4+54​+254​+1254​+…

Find the indicated term of the geometric sequence. -a1 = 6, r = -2; find a11a _ { 11 }a11​

Evaluate the combination. - (52)\left( \begin{array} { l } 5 \\2\end{array} \right)(52​)