Question 1

Find the indicated quantity of the arithmetic sequence.
-a1 = 5 , d = -3 ; find $a _ { 8 }$

Accepted Answer

A) 26 
B) -16 
C) 29 
D) -19 
A) 26 
B) -16 
C) 29 
D) -19 B

Question 2

Write the next three terms of the sequence.
-5, 9, 13, 17, ...

Accepted Answer

A) 25, 29, 33 
B) 13, 9, 5 
C) 21, 25, 29 
D) 21, 25, 33 
A) 25, 29, 33 
B) 13, 9, 5 
C) 21, 25, 29 
D) 21, 25, 33 C

Question 3

Use the binomial theorem to expand the expression.
-$( x + 4 y ) ^ { 3 }$

Accepted Answer

A)  $x ^ { 3 } + 64 y ^ { 3 }$ 
B)  $x ^ { 3 } + 4 x ^ { 2 } y + 8 x y + 16 x y ^ { 2 } + 32 y ^ { 2 } + 64 y ^ { 3 }$ 
C)  $x ^ { 3 } + 12 x ^ { 2 } y + 48 x y ^ { 2 } + 64 y ^ { 3 }$ 
D)  $3 x + 12 y$ 
A)  $x ^ { 3 } + 64 y ^ { 3 }$ 
B)  $x ^ { 3 } + 4 x ^ { 2 } y + 8 x y + 16 x y ^ { 2 } + 32 y ^ { 2 } + 64 y ^ { 3 }$ 
C)  $x ^ { 3 } + 12 x ^ { 2 } y + 48 x y ^ { 2 } + 64 y ^ { 3 }$ 
D)  $3 x + 12 y$ C

Question 4

Determine the first five terms of the geometric sequence.
-a1 = 6, r = -4

Accepted Answer

A) 6, 2, -2, -6, -10 
B) 6, -24, 96, -384, 1536 
C) 6, 24, 96, -384, 1536 
D) -4, -24, 96, -384, 1536 
A) 6, 2, -2, -6, -10 
B) 6, -24, 96, -384, 1536 
C) 6, 24, 96, -384, 1536 
D) -4, -24, 96, -384, 1536

Question 5

Use the binomial theorem to expand the expression.
-$( 4 x + 1 ) ^ { 5 }$

Accepted Answer

A)  $1024 x ^ { 5 } + 1$ 
B)  $1024 x ^ { 5 } + 256 x ^ { 4 } + 64 x ^ { 3 } + 16 x ^ { 2 } + 4 x + 1$ 
C)  $1024 x ^ { 5 } + 20 x ^ { 4 } + 160 x ^ { 3 } + 160 x ^ { 2 } + 20 x + 1$ 
D)  $1024 x ^ { 5 } + 1280 x ^ { 4 } + 640 x ^ { 3 } + 160 x ^ { 2 } + 20 x + 1$ 
A)  $1024 x ^ { 5 } + 1$ 
B)  $1024 x ^ { 5 } + 256 x ^ { 4 } + 64 x ^ { 3 } + 16 x ^ { 2 } + 4 x + 1$ 
C)  $1024 x ^ { 5 } + 20 x ^ { 4 } + 160 x ^ { 3 } + 160 x ^ { 2 } + 20 x + 1$ 
D)  $1024 x ^ { 5 } + 1280 x ^ { 4 } + 640 x ^ { 3 } + 160 x ^ { 2 } + 20 x + 1$

Question 6

Write the word or phrase that best completes each statement or answers the question.
Use mathematical induction to prove the following statement for all positive integers n.
-$1 + 6 + 6 ^ { 2 } + \ldots + 6 ^ { n - 1 } = \frac { 6 ^ { n } - 1 } { 5 }$

Accepted Answer

Condition 1:For n = 1, we get 1, we get

Question 7

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.
-$a = - 10 , d = 3 ; \quad \text { find } a _ { n } \text { and } a _ { 7 }$

Accepted Answer

A)  $a _ { n } = - 13 - 3 n , a _ { 7 } = 8$ 
B)  $a _ { n } = - 13 + 3 n , a _ { 7 } = 8$ 
C)  $a _ { n } = - 10 + 3 n , a _ { 7 } = 8$ 
D)  $a _ { n } = - 13 + 3 n , a _ { 7 } = 32$ 
A)  $a _ { n } = - 13 - 3 n , a _ { 7 } = 8$ 
B)  $a _ { n } = - 13 + 3 n , a _ { 7 } = 8$ 
C)  $a _ { n } = - 10 + 3 n , a _ { 7 } = 8$ 
D)  $a _ { n } = - 13 + 3 n , a _ { 7 } = 32$

Question 8

Write out the series.
-$\sum _ { n = 1 } ^ { 5 } \frac { n + 1 } { n + 2 }$

Accepted Answer

A)  $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 }$ 
B)  $\frac { 6 } { 7 }$ 
C)  $\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 }$ 
D)  $\frac { 1 } { 3 } + \frac { 2 } { 4 } + \frac { 3 } { 5 } + \frac { 4 } { 6 }$ 
A)  $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 }$ 
B)  $\frac { 6 } { 7 }$ 
C)  $\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 }$ 
D)  $\frac { 1 } { 3 } + \frac { 2 } { 4 } + \frac { 3 } { 5 } + \frac { 4 } { 6 }$

Question 9

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.
-8, 14, 20, 26, . . ., 242

Accepted Answer

A) 5010 
B) 5000 
C) 248 
D) 5120 
A) 5010 
B) 5000 
C) 248 
D) 5120

Question 10

Evaluate the expression.
-${ } _ { 8 } \mathrm { P } _ { 5 }$

Accepted Answer

A) 8 
B) 5 
C) 6720 
D) 336 
A) 8 
B) 5 
C) 6720 
D) 336

Question 11

Find the sum of the terms in the geometric sequence.
-54, 18, 6, 2, . . .

Accepted Answer

A) 54 
B) 81 
C) 78 
D) - 27 
A) 54 
B) 81 
C) 78 
D) - 27

Question 12

Evalutate the series.
-$$\sum _ { n = 4 } ^ { 7 } 7 n$$

Accepted Answer

A) 105 
B) 154 
C) 49 
D) 77 
A) 105 
B) 154 
C) 49 
D) 77

Question 13

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.
-$a _ { 1 } = - 8 , d = - 12 ; \text { find } s _ { 6 }$

Accepted Answer

A) 228 
B) -120 
C) - 228 
D) -60 
A) 228 
B) -120 
C) - 228 
D) -60

Question 14

Solve the problem.
-A grocery store display of apples has a total of 16 rows. The bottom row requires 103 apples. Each successive row requires 5 less apples than the prior one. How many apples are required to build the display?

Accepted Answer

A) 1048 apples 
B) 2248 apples 
C) 1008 apples 
D) 2096 apples 
A) 1048 apples 
B) 2248 apples 
C) 1008 apples 
D) 2096 apples

Question 15

Solve the problem.
-If a club consists of 9 members, how many different arrangements of president and vice-president are possible?

Accepted Answer

A) 181,440 
B) 72 
C) 7 
D) 9 
A) 181,440 
B) 72 
C) 7 
D) 9

Question 16

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.
-$a _ { 1 } = 5 , d = 4 ; \text { find } s 60$

Accepted Answer

A) 7500 
B) 7257 
C) 7380 
D) 6875 
A) 7500 
B) 7257 
C) 7380 
D) 6875

Question 17

Solve the problem.
-Find the number of permutations of the letters in the word DOUBLE.

Accepted Answer

A) 24 
B) 120 
C) 5 
D) 1 
A) 24 
B) 120 
C) 5 
D) 1

Question 18

Find the indicated term of the sequence whose nth term is shown.
-$a _ { n } = 2 n - 3 , \text { twelfth term }$

Accepted Answer

A) 35 
B) 33 
C) 39 
D) 36 
A) 35 
B) 33 
C) 39 
D) 36

Question 19

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data.
-10, 20, 30, 40, 50

Accepted Answer

A) 30 
B) 150 
C) 40 
D) 20 
A) 30 
B) 150 
C) 40 
D) 20

Question 20

Solve the problem.
-A traffic light is red for 50 seconds, yellow for 5 seconds, and green for 40 seconds. Find the probability: P(the light is green)

Accepted Answer

A)  $\frac { 1 } { 95 }$ 
B)  $\frac { 1 } { 28 }$ 
C)  $\frac { 1 } { 14 }$ 
D)  $\frac { 1 } { 19 }$ 
A)  $\frac { 1 } { 95 }$ 
B)  $\frac { 1 } { 28 }$ 
C)  $\frac { 1 } { 14 }$ 
D)  $\frac { 1 } { 19 }$

Find the indicated quantity of the arithmetic sequence. -a1 = 5 , d = -3 ; find $a _ { 8 }$

Write the next three terms of the sequence. -5, 9, 13, 17, ...

Use the binomial theorem to expand the expression. - $( x + 4 y ) ^ { 3 }$

Determine the first five terms of the geometric sequence. -a1 = 6, r = -4

Use the binomial theorem to expand the expression. - $( 4 x + 1 ) ^ { 5 }$

Write the word or phrase that best completes each statement or answers the question. Use mathematical induction to prove the following statement for all positive integers n. - $1 + 6 + 6 ^ { 2 } + \ldots + 6 ^ { n - 1 } = \frac { 6 ^ { n } - 1 } { 5 }$

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the arithmetic sequence. - $a = - 10 , d = 3 ; \quad \text { find } a _ { n } \text { and } a _ { 7 }$

Write out the series. - $\sum _ { n = 1 } ^ { 5 } \frac { n + 1 } { n + 2 }$

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. -8, 14, 20, 26, . . ., 242

Evaluate the expression. - ${ } _ { 8 } \mathrm { P } _ { 5 }$

Find the sum of the terms in the geometric sequence. -54, 18, 6, 2, . . .

Evalutate the series. - $\sum _ { n = 4 } ^ { 7 } 7 n$

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. - $a _ { 1 } = - 8 , d = - 12 ; \text { find } s _ { 6 }$

Solve the problem. -A grocery store display of apples has a total of 16 rows. The bottom row requires 103 apples. Each successive row requires 5 less apples than the prior one. How many apples are required to build the display?

Solve the problem. -If a club consists of 9 members, how many different arrangements of president and vice-president are possible?

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. - $a _ { 1 } = 5 , d = 4 ; \text { find } s 60$

Solve the problem. -Find the number of permutations of the letters in the word DOUBLE.

Find the indicated term of the sequence whose nth term is shown. - $a _ { n } = 2 n - 3 , \text { twelfth term }$

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data. -10, 20, 30, 40, 50

Solve the problem. -A traffic light is red for 50 seconds, yellow for 5 seconds, and green for 40 seconds. Find the probability: P(the light is green)

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

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Exam 12: Sequences, Series, and Probability

Find the indicated quantity of the arithmetic sequence. -a1 = 5 , d = -3 ; find a8a _ { 8 }a8​