Question 1

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = ( 2 + n ) ^ { 1 / n }$$

Accepted Answer

A)  Diverges 
B)  Converges 
A)  Diverges 
B)  Converges

Question 2

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = 54 \mathrm { e } ^ { n }$$

Accepted Answer

A)  Converges 
B)  Diverges 
A)  Converges 
B)  Diverges

Question 3

Solve the problem.
-If the police have 9 suspects, how many different sets of 5 suspects can they select for a lineup?

Accepted Answer

A)  126 
B)  15,120 
C)  45 
D)  3024 
A)  126 
B)  15,120 
C)  45 
D)  3024

Question 4

Find the common ratio r for the given infinite geometric sequence.
-A sequence of yearly payments of $3000 is invested at an interest rate of 1.5%, compounded annually. What is the total amount of the annuity after 9 years?

Accepted Answer

A)  $28,178.00 
B)  $29,678.00 
C)  $28,678.00 
D)  $27,678.00 
A)  $28,178.00 
B)  $29,678.00 
C)  $28,678.00 
D)  $27,678.00

Question 5

Provide an appropriate response.
-The sum of an infinite geometric series exists if:

Accepted Answer

A)  $| r | \leq 1$ 
B)  $| \mathrm { r } |  1$ 
A)  $| r | \leq 1$ 
B)  $| \mathrm { r } |  1$

Question 6

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-

Accepted Answer

A)  $a _ { n } = n + 2$ 
B)  $a _ { n } = n + 1$ 
C)  $a _ { n } = n - 3$ 
D)  $a _ { n } = 3 - n$ 
A)  $a _ { n } = n + 2$ 
B)  $a _ { n } = n + 1$ 
C)  $a _ { n } = n - 3$ 
D)  $a _ { n } = 3 - n$

Question 7

Find the first six terms of the sequence.
-$$a _ { 1 } = 2 , a _ { n } = 3 \cdot a _ { n - 1 }$$

Accepted Answer

A)  $0,3,6,9,12,15$ 
B)  $2,6,18,54,162,486$ 
C)  $6,18,54,162,486,1458$ 
D)  $2,6,9,12,15,18$ 
A)  $0,3,6,9,12,15$ 
B)  $2,6,18,54,162,486$ 
C)  $6,18,54,162,486,1458$ 
D)  $2,6,9,12,15,18$

Question 8

Find the nth term of the geometric sequence.
-$2 , - 6,18 , \ldots ; n = 11$

Accepted Answer

A)  59,049 
B)  $1,062,882$ 
C)  $- 39,366$ 
D)  118,098 
A)  59,049 
B)  $1,062,882$ 
C)  $- 39,366$ 
D)  118,098

Question 9

Find the future value of the annuity.
-There are payments of $100 at the end of each year for 11 years at 3% interest compounded annually

Accepted Answer

A)  $1280.78 
B)  $4614.11 
C)  $1146.39 
D)  $447.97 
A)  $1280.78 
B)  $4614.11 
C)  $1146.39 
D)  $447.97

Question 10

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = \frac { n - 15 } { 2 n }$$

Accepted Answer

A)  Diverges 
B)  Converges 
A)  Diverges 
B)  Converges

Question 11

Evaluate the sum.
-$\sum _ { j = 1 } ^ { 10 } ( 7 j - 5 )$

Accepted Answer

A)  335 
B)  310 
C)  270 
D)  380 
A)  335 
B)  310 
C)  270 
D)  380

Question 12

Find the future value of the annuity.
-A sequence of yearly payments of $6000 is invested at the end of each of 11 years at an interest rate of 2.1%, compounded annually. What is the total amount of the annuity after 11 years?

Accepted Answer

A)  $72,885.48 
B)  $74,385.48 
C)  $72,385.48 
D)  $73,385.48 
A)  $72,885.48 
B)  $74,385.48 
C)  $72,385.48 
D)  $73,385.48

Question 13

Evaluate the sum using the given information.
-$$\begin{array} { l } 
\mathrm { x } _ { 1 } = - 3 , \mathrm { x } _ { 2 } = - 4 , \mathrm { x } _ { 3 } = 0 , \mathrm { x } _ { 4 } = 4 , \text { and } \Delta \mathrm { x } = 0.9 ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 \
\sum _ { \mathrm { i } = 1 } ^ { 4 } \mathrm { f } \left( \mathrm { x } _ { \mathrm { i } } \right) \Delta \mathrm { x }
\end{array}$$

Accepted Answer

A)  75.6 
B)  18.9 
C)  16.4934 
D)  19.9 
A)  75.6 
B)  18.9 
C)  16.4934 
D)  19.9

Question 14

Evaluate the series, if it converges.
-$$\sum _ { \mathrm { k } = 1 } ^ { \infty } \left( \frac { 3 } { 4 } \right) ^ { \mathrm { k } }$$

Accepted Answer

A)  $- 3$ 
B)  Does not converge. 
C)  3 
D)  4 
A)  $- 3$ 
B)  Does not converge. 
C)  3 
D)  4

Question 15

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).
-$$a _ { 13 } = - 97 , a _ { 15 } = - 299$$

Accepted Answer

A)  $a _ { n } = 1115 + 101 ( n - 1 ) , a _ { 6 } = 5963$ 
B)  $a _ { n } = 1115 - 101 ( n - 1 ) , a _ { 6 } = 509$ 
C)  $a _ { n } = 1115 - 101 ( n - 1 ) , a _ { 6 } = 1721$ 
D)  $a _ { n } = 1115 - 101 ( n - 1 ) , a _ { 6 } = 610$ 
A)  $a _ { n } = 1115 + 101 ( n - 1 ) , a _ { 6 } = 5963$ 
B)  $a _ { n } = 1115 - 101 ( n - 1 ) , a _ { 6 } = 509$ 
C)  $a _ { n } = 1115 - 101 ( n - 1 ) , a _ { 6 } = 1721$ 
D)  $a _ { n } = 1115 - 101 ( n - 1 ) , a _ { 6 } = 610$

Question 16

Find the first six terms of the sequence.
-$a _ { 1 } = 6 , a _ { 2 } = 7 ;$ for $n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Accepted Answer

A)  $6,7,13,14,20,20$ 
B)  $6,7,12,18,24,30$ 
C)  $6,7,42,294,12,348,3,630,312$ 
D)  $6,7,13,20,33,53$ 
A)  $6,7,13,14,20,20$ 
B)  $6,7,12,18,24,30$ 
C)  $6,7,42,294,12,348,3,630,312$ 
D)  $6,7,13,20,33,53$

Question 17

Solve the problem.
-There are 5 women running in a race. How many first, second, and third place possibilities can occur?

Accepted Answer

A)  10 
B)  15 
C)  125 
D)  60 
A)  10 
B)  15 
C)  125 
D)  60

Question 18

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { k = 3 } ^ { 6 } ( 2 k - 3 )$$

Accepted Answer

A)  21 
B)  27 
C)  24 
D)  15 
A)  21 
B)  27 
C)  24 
D)  15

Question 19

Find the common ratio r for the given infinite geometric sequence.
-3, -9, 27, -81, 243, . . .

Accepted Answer

A)  -12 
B)  3 
C) $$- \frac { 1 } { 3 }$$ 
D)  -3 
A)  -12 
B)  3 
C) $$- \frac { 1 } { 3 }$$ 
D)  -3

Question 20

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$S _ { 9 } = - 306 , a _ { 9 } = - 70$

Accepted Answer

A)  $a _ { 1 } = 2 , d = - 9$ 
B)  $\mathrm { a } _ { 1 } = 562 , \mathrm {~d} = - 9$ 
C)  $a _ { 1 } = 2 , d = - 15.56$ 
D)  $\mathrm { a } _ { 1 } = 562 , \mathrm {~d} = - 15.56$ 
A)  $a _ { 1 } = 2 , d = - 9$ 
B)  $\mathrm { a } _ { 1 } = 562 , \mathrm {~d} = - 9$ 
C)  $a _ { 1 } = 2 , d = - 15.56$ 
D)  $\mathrm { a } _ { 1 } = 562 , \mathrm {~d} = - 15.56$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = ( 2 + n ) ^ { 1 / n }$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = 54 \mathrm { e } ^ { n }$

Solve the problem. -If the police have 9 suspects, how many different sets of 5 suspects can they select for a lineup?

Find the common ratio r for the given infinite geometric sequence. -A sequence of yearly payments of $3000 is invested at an interest rate of 1.5%, compounded annually. What is the total amount of the annuity after 9 years?

Provide an appropriate response. -The sum of an infinite geometric series exists if:

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Find the first six terms of the sequence. - $a _ { 1 } = 2 , a _ { n } = 3 \cdot a _ { n - 1 }$

Find the nth term of the geometric sequence. - $2 , - 6,18 , \ldots ; n = 11$

Find the future value of the annuity. -There are payments of $100 at the end of each year for 11 years at 3% interest compounded annually

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = \frac { n - 15 } { 2 n }$

Evaluate the sum. - $\sum _ { j = 1 } ^ { 10 } ( 7 j - 5 )$

Find the future value of the annuity. -A sequence of yearly payments of $6000 is invested at the end of each of 11 years at an interest rate of 2.1%, compounded annually. What is the total amount of the annuity after 11 years?

Evaluate the sum using the given information. - =-3,=-4,=0,=4, and \Delta=0.9;()=-5 \Delta

Evaluate the series, if it converges. - $\sum _ { \mathrm { k } = 1 } ^ { \infty } \left( \frac { 3 } { 4 } \right) ^ { \mathrm { k } }$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $a _ { 13 } = - 97 , a _ { 15 } = - 299$

Find the first six terms of the sequence. - $a _ { 1 } = 6 , a _ { 2 } = 7 ;$ for $n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Solve the problem. -There are 5 women running in a race. How many first, second, and third place possibilities can occur?

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { k = 3 } ^ { 6 } ( 2 k - 3 )$

Find the common ratio r for the given infinite geometric sequence. -3, -9, 27, -81, 243, . . .

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $S _ { 9 } = - 306 , a _ { 9 } = - 70$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Filters

Exam 12: Further Topics in Algebra

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - an=(2+n)1/na _ { n } = ( 2 + n ) ^ { 1 / n }an​=(2+n)1/n

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - an=54ena _ { n } = 54 \mathrm { e } ^ { n }an​=54en