Intermediate Algebra

John Hornsby; Terry McGinnis; Margaret L. Lial

Chapter 11 Further Topics in Algebra - all with Video Answers

Educators

Section 1

Sequences and Series

01:29

Problem 1

Fill in each blank with the correct response.
The domain of an infinite sequence is __________.

Gregory Higby

Numerade Educator

00:51

Problem 2

Fill in each blank with the correct response.
In the sequence $3,6,9,12,$ the term $a_{3}=$ ________.

Vysakh M

Numerade Educator

00:56

Problem 3

Fill in each blank with the correct response.
If $a_{n}=2 n,$ then $a_{40}=$ _________.

Vysakh M

Numerade Educator

00:59

Problem 4

Fill in each blank with the correct response.
If $a_{n}=(-1)^{n},$ then $a_{115}=$ __________.

Vysakh M

Numerade Educator

01:14

Problem 5

Fill in each blank with the correct response.
The value of the sum $\sum_{i=1}^{3}(i+2)$ is _________.

Gregory Higby

Numerade Educator

00:55

Problem 6

Fill in each blank with the correct response.
The arithmetic mean of $-4,-2,0,2,$ and 4 is __________.

Vysakh M

Numerade Educator

00:35

Problem 7

Write the first five terms of each sequence.
$$
a_{n}=n+1
$$

Maninder Singh

Numerade Educator

00:28

Problem 8

Write the first five terms of each sequence.
$$
a_{n}=n+4
$$

Maninder Singh

Numerade Educator

00:57

Problem 9

Write the first five terms of each sequence.
$$
a_{n}=\frac{n+3}{n}
$$

Maninder Singh

Numerade Educator

01:07

Problem 10

Write the first five terms of each sequence.
$$
a_{n}=\frac{n+2}{n}
$$

Julie Silva

Numerade Educator

00:39

Problem 11

Write the first five terms of each sequence.
$$
a_{n}=3^{n}
$$

Maninder Singh

Numerade Educator

00:31

Problem 12

Write the first five terms of each sequence.
$$
a_{n}=2^{n}
$$

Amy Jiang

Numerade Educator

01:10

Problem 13

Write the first five terms of each sequence.
$$
a_{n}=-\frac{1}{n^{2}}
$$

Vysakh M

Numerade Educator

01:03

Problem 14

Write the first five terms of each sequence.
$$
a_{n}=-\frac{2}{n^{2}}
$$

Maninder Singh

Numerade Educator

01:23

Problem 15

Write the first five terms of each sequence.
$$
a_{n}=5(-1)^{n-1}
$$

Maninder Singh

Numerade Educator

01:04

Problem 16

Write the first five terms of each sequence.
$$
a_{n}=6(-1)^{n+1}
$$

Maninder Singh

Numerade Educator

00:47

Problem 17

Write the first five terms of each sequence.
$$
a_{n}=n-\frac{1}{n}
$$

Maninder Singh

Numerade Educator

00:56

Problem 18

Write the first five terms of each sequence.
$$
a_{n}=n+\frac{4}{n}
$$

Maninder Singh

Numerade Educator

00:20

Problem 19

Find the indicated term for each sequence.
$a_{n}=-9 n+2 ; \quad a_{8}$

Maninder Singh

Numerade Educator

00:55

Problem 20

Find the indicated term for each sequence.
$$
a_{n}=-3 n+7 ; \quad a_{12}
$$

Vysakh M

Numerade Educator

00:41

Problem 21

Find the indicated term for each sequence.
$$
a_{n}=\frac{3 n+7}{2 n-5} ; \quad a_{14}
$$

Maninder Singh

Numerade Educator

00:40

Problem 22

Find the indicated term for each sequence.
$$
a_{n}=\frac{5 n-9}{3 n+8} ; \quad a_{16}
$$

Maninder Singh

Numerade Educator

00:39

Problem 23

Find the indicated term for each sequence.
$$
a_{n}=(n+1)(2 n+3) ; \quad a_{8}
$$

Maninder Singh

Numerade Educator

00:52

Problem 24

Find the indicated term for each sequence.
$$
a_{n}=(5 n-2)(3 n+1) ; \quad a_{10}
$$

Maninder Singh

Numerade Educator

01:28

Problem 25

Determine an expression for the general term $a_{n}$ of each sequence.
$$
4,8,12,16, \ldots
$$

Vysakh M

Numerade Educator

01:10

Problem 26

Determine an expression for the general term $a_{n}$ of each sequence.
$$
7,14,21,28, \ldots
$$

Vysakh M

Numerade Educator

01:30

Problem 27

Determine an expression for the general term $a_{n}$ of each sequence.
$$
-8,-16,-24,-32, \ldots
$$

Vysakh M

Numerade Educator

01:10

Problem 28

Determine an expression for the general term $a_{n}$ of each sequence.
$$
-10,-20,-30,-40, \ldots
$$

Vysakh M

Numerade Educator

01:11

Problem 29

Determine an expression for the general term $a_{n}$ of each sequence.
$$
\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \frac{1}{81}, \ldots
$$

Vysakh M

Numerade Educator

01:06

Problem 30

Determine an expression for the general term $a_{n}$ of each sequence.
$$
\frac{2}{5}, \frac{2}{25}, \frac{2}{125}, \frac{2}{625}, \ldots
$$

Vysakh M

Numerade Educator

01:40

Problem 31

Determine an expression for the general term $a_{n}$ of each sequence.
$$
\frac{2}{5}, \frac{3}{6}, \frac{4}{7}, \frac{5}{8}, \ldots
$$

Vysakh M

Numerade Educator

01:18

Problem 32

Determine an expression for the general term $a_{n}$ of each sequence.
$$
\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots
$$

Vysakh M

Numerade Educator

03:38

Solve each applied problem by writing the first few terms of a sequence.
Horacio borrows $\$ 1000$ and agrees to pay $\$ 100$ plus interest of $1 \%$ on the unpaid balance each month. Find the payments for the first six months and the remaining debt at the end of that period.

Kathleen Luttrell

Numerade Educator

02:22

Problem 34

Solve each applied problem by writing the first few terms of a sequence.
Leslie is offered a new job with a salary of $20,000+2500 n$ dollars per year at the end of the $n$ th year. Write a sequence showing her salary at the end of each of the first 5 yr. If she continues in this way, what will her salary be at the end of the tenth year?

Kathleen Luttrell

Numerade Educator

01:37

Problem 35

Solve each applied problem by writing the first few terms of a sequence.
Suppose that an automobile loses $\frac{1}{5}$ of its value each year; that is, at the end of any given year, the value is $\frac{4}{5}$ of the value at the beginning of that year. If a car costs $\$ 20,000$ new, what is its value at the end of $5 \mathrm{yr}$, to the nearest dollar?

Margaret Farmer

Numerade Educator

00:50

Problem 36

Solve each applied problem by writing the first few terms of a sequence.
A certain car loses $\frac{1}{2}$ of its value each year. If this car cost $\$ 40,000$ new, what is its value at the end of 6 yr?

Margaret Farmer

Numerade Educator

01:34

Problem 37

Write each series as a sum of terms and then find the sum.
$$
\sum_{i=1}^{5}(i+3)
$$

Gregory Higby

Numerade Educator

01:30

Problem 38

Write each series as a sum of terms and then find the sum.
$$
\sum_{i=1}^{6}(i+9)
$$

Gregory Higby

Numerade Educator

01:20

Problem 39

Write each series as a sum of terms and then find the sum.
$$
\sum_{i=1}^{3}\left(i^{2}+2\right)
$$

Gregory Higby

Numerade Educator

01:59

Problem 40

Write each series as a sum of terms and then find the sum.
$$
\sum_{i=1}^{4}\left(i^{3}+3\right)
$$

Gregory Higby

Numerade Educator

01:58

Problem 41

Write each series as a sum of terms and then find the sum.
$$
\sum_{i=1}^{6}(-1)^{i} \cdot 2
$$

Gregory Higby

Numerade Educator

02:02

Problem 42

Write each series as a sum of terms and then find the sum.
$$
\sum_{i=1}^{5}(-1)^{i} \cdot i
$$

Gregory Higby

Numerade Educator

02:02

Problem 43

Write each series as a sum of terms and then find the sum.
$$
\sum_{i=3}^{7}(i-3)(i+2)
$$

Gregory Higby

Numerade Educator

02:01

Problem 44

Write each series as a sum of terms and then find the sum.
$$
\sum_{i=2}^{6}(i+3)(i-4)
$$

Gregory Higby

Numerade Educator

01:06

Problem 45

Write each series using summation notation.
$$
3+4+5+6+7
$$

Nick Johnson

Numerade Educator

00:34

Problem 46

Write each series using summation notation.
$$
7+8+9+10+11
$$

Maninder Singh

Numerade Educator

01:14

Problem 47

Write each series using summation notation.
$$
-2+4-8+16-32
$$

Nick Johnson

Numerade Educator

01:13

Problem 48

Write each series using summation notation.
$$
-1+2-3+4-5+6
$$

Ankit Gupta

Numerade Educator

00:39

Problem 49

Write each series using summation notation.
$$
1+4+9+16
$$

Maninder Singh

Numerade Educator

00:40

Problem 50

Write each series using summation notation.
$$
1+16+81+256
$$

Maninder Singh

Numerade Educator

02:37

Problem 51

When asked to write the series $-1-4-9-16-25$ using summation notation, a student incorrectly wrote the following.
$$
\sum_{t=1}^{5}(-i)^{2}
$$
Give the correct summation notation.

Hira Saeed

Numerade Educator

01:51

Problem 52

When asked to write the first five terms of the sequence defined by $a_{n}=5 n-1,$ a student incorrectly wrote the following.
$$
4+9+14+19+24
$$
Give the correct answer.

Hira Saeed

Numerade Educator

01:38

Problem 53

Find the arithmetic mean for each set of values.
$$
8,11,14,9,7,6,8
$$

Gregory Higby

Numerade Educator

01:28

Problem 54

Find the arithmetic mean for each set of values.
$$
10,12,8,19,23,12
$$

Gregory Higby

Numerade Educator

01:39

Problem 55

Find the arithmetic mean for each set of values.
$$
5,9,8,2,4,7,3,2,0
$$

Gregory Higby

Numerade Educator

01:33

Problem 56

Find the arithmetic mean for each set of values.
$$
2,1,4,8,3,7,10,8,0
$$

Gregory Higby

Numerade Educator

01:09

Problem 57

Solve each problem.
The number of mutual funds operating in the United States each year during the period 2012 through 2016 is given in the table. To the nearest whole number, what was the average number of mutual funds operating per year during the given period?
$$
\begin{array}{|c|c|}
\hline \text { Year } & \text { Number of Mutual Funds } \\
\hline 2012 & 8744 \\
2013 & 8972 \\
2014 & 9258 \\
2015 & 9517 \\
2016 & 9511 \\
\hline
\end{array}
$$

Kathleen Luttrell

Numerade Educator

01:17

Problem 58

Solve each problem.
The total assets of mutual funds operating in the United States, in billions of dollars, for each year during the period 2012 through 2016 are shown in the table. What were the average assets per year during this period?
$$
\begin{array}{|c|c|}
\hline \text { Year } & \text { Assets (in billions of dollars) } \\
2012 & 13,054 \\
2013 & 15,049 \\
2014 & 15,873 \\
2015 & 15,650 \\
2016 & 16,344 \\
\hline
\end{array}
$$

Kathleen Luttrell

Numerade Educator

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

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Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

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Problem 51

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Problem 58