We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Pre-Calculus

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Sequences And Series

Find the sum, if possible:

1-3+9-27+...

Possible Answers:

6725

7625

5267

No solution

2765

Correct answer:

No solution

Explanation:

The formula for the summation of an infinite geometric series is

$S= \frac{a_1}{1-r}$ ,

where a_1 is the first term in the series and is the rate of change between succesive terms in a series.

In order for an infinite geometric series to have a sum, needs to be greater than and less than , i.e. -1<r<1 .

Since r=-3 , there is no solution.

Report an Error

Example Question #2 : Sequences And Series

Determine the summation notation for the following series:

3+9+27+81+243

Possible Answers:

$\sum_{n=1}^{5}3^{n}$

$\sum_{n=1}^{5}3$

$\sum_{n=1}^{5}n^3$

$\sum_{n=1}^{\infty }n^{3}$

$\sum_{n=1}^{\infty }3^{n}$

Correct answer:

$\sum_{n=1}^{5}3^{n}$

Explanation:

The series is a geometric series. The summation notation of a geometric series is

$\sum_{n=1}^{n}a_{1}\cdot r^{n-1}$ ,

where is the number of terms in the series, $a_{1}$ is the first term of the series, and is the common ratio between terms.

In this series, is , $a_{1}$ is , and is . Therefore, the summation notation of this geometric series is:

$\sum_{n=1}^{5}3\cdot 3^{n-1}$

This simplifies to:

$\sum_{n=1}^{5}3^{n}$

Report an Error

Example Question #1 : Sequences And Series

Determine the summation notation for the following series:

$10-5+\frac{5}{2}-\frac{5}{4}+\frac{5}{8}$

Possible Answers:

$\sum_{n=1}^{5}-10\cdot (-\frac{1}{2})^{n}$

$\sum_{n=1}^{5}-20\cdot (-\frac{1}{2})^{n}$

$\sum_{n=1}^{5}-20\cdot (\frac{1}{2})^{n}$

$\sum_{n=1}^{5}20\cdot (-\frac{1}{2})^{n}$

$\sum_{n=1}^{\infty }-20\cdot (-\frac{1}{2})^{n}$

Correct answer:

$\sum_{n=1}^{5}-20\cdot (-\frac{1}{2})^{n}$

Explanation:

The series is a geometric series. The summation notation of a geometric series is

$\sum_{n=1}^{n}a_{1}\cdot r^{n-1}$ ,

where is the number of terms in the series, $a_{1}$ is the first term of the series, and is the common ratio between terms.

In this series, is , $a_{1}$ is , and is $-\frac{1}{2}$ . Therefore, the summation notation of this geometric series is:

$\sum_{n=1}^{5}10\cdot (-\frac{1}{2})^{n-1}$

This simplifies to:

$\sum_{n=1}^{5}10\cdot (-\frac{1}{2})^{n}\cdot (-\frac{1}{2})^{-1}$

$\sum_{n=1}^{5}10\cdot (-\frac{1}{2})^{n}\cdot (-2)$

$\sum_{n=1}^{5}-20\cdot (-\frac{1}{2})^{n}$

Report an Error

Example Question #1 : Sequences And Series

Indicate the sum of the following series:

$\sum_{x=1}^{7}(4x-5)$

Possible Answers:

111

Correct answer:

Explanation:

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(2(a_1)+(n-1)d)$ ,

where a_1 is the first value in the series, is the number of terms in the series, and is the difference between sequential terms in the series.

In this problem we have:

a_1 = -1

d = 4

n=7

Plugging in our values, we get:

$S = \frac{7}{2}(2(-1)+(6)4)$

S = 3.5(-2+24)

S = 77

Report an Error

Example Question #1 : Sequences And Series

Indicate the sum of the following series:

$\sum_{c=3}^{10}(8-5c)$

Possible Answers:

Correct answer:

Explanation:

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(2(a_1)+(n-1)d)$ ,

where a_1 is the first value in the series, is the number of terms in the series, and is the difference between sequential terms in the series.

Here we have:

a_1 = -7

n=8

d = -5

Plugging in our values, we get:

$S = \frac{8}{2}(2(-7)+(8-1)-5)$

S=4(-14-35)

S=-196

Report an Error

Example Question #2 : Using Sigma Notation

Indicate the sum of the following series:

$\sum_{m=-2}^{9}(2)^m$

Possible Answers:

1230.75

1302.75

1000.25

1023.75

1032.25

Correct answer:

1023.75

Explanation:

The formula for the sum of a geometric series is

$S=\frac{a_1-a_1r^n}{1-r}$ ,

where a_1 is the first term in the series, is the rate of change between sequential terms, and is the number of terms in the series

For this problem, these values are:

$a_1 = \frac{1}{4}$

r = 2

n = 12

Plugging in our values, we get:

$S=\frac{\frac{1}{4}-\frac{1}{4}(2)^{12}}{1-2}$

S = 1023.75

Report an Error

Example Question #1 : Using Sigma Notation

Indicate the sum of the following series.

$\sum_{b=2}^{11} \frac{1}{2}(4)^{b-2}$

Possible Answers:

172,764.5

174,726.5

176,742.5

164,772.5

174,762.5

Correct answer:

174,762.5

Explanation:

The formula for the sum of a geometric series is

$S=\frac{a_1-a_1r^n}{1-r}$ ,

where a_1 is the first term in the series, is the rate of change between sequential terms, and is the number of terms in the series

In this problem we have:

$a_1 = \frac{1}{2}$

r = 4

n = 10

Plugging in our values, we get:

$S=\frac{\frac{1}{2}-\frac{1}{2}(4)^{10}}{1-4}$

S = 174,762.5

Report an Error

Example Question #11 : Sequences And Series

Consider the sequence: $2,\ 5,\ 8,\ 11,\ ...$

What is the fifteenth term in the sequence?

Possible Answers:

Correct answer:

Explanation:

The sequence can be described by the equation $\small 2+3(n-1)$ , where is the term in the sequence.

For the 15th term, n=15 .

$\small 2+3(n-1)=2+3(15-1)$

2+3(14)

2+42

Report an Error

Example Question #12 : Sequences And Series

What are the first three terms in the series?

$\sum_{n=1}^{7}(4n-5)$

Possible Answers:

(1)+(3)+(7)

(-5)+(-1)+(3)

(-1)+(3)+(8)

(-1)+(3)+(7)

(3)+(7)+(11)

Correct answer:

(-1)+(3)+(7)

Explanation:

To find the first three terms, replace with , , and .

(4n-5) = (4(1)-5)=-1

(4n-5) = (4(2)-5)=3

(4n-5) = (4(3)-5)=7

The first three terms are , , and .

Report an Error

Example Question #1 : Finding Terms In A Series

Find the first three terms in the series.

$\sum_{n=3}^{10}(8-5n)$

Possible Answers:

(3)+(-2)+(-7)

(-2)+(-7)+(-12)

(-7)+(12)+(-17)

(-7)+(-12)+(-17)

(7)+(12)+(17)

Correct answer:

(-7)+(-12)+(-17)

Explanation:

To find the first three terms, replace with , , and .

(8-5n) = (8-5(3))=-7

(8-5n) = (8-5(4))=-12

(8-5n) = (8-5(5))=-17

The first three terms are , , and .

Report an Error

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

View Tutors

Angela
Certified Tutor

North Georgia College State University, Bachelor of Science, Special Education. North Georgia College State University, Mas...

View Tutors

Dereika
Certified Tutor

Southern University and A & M College, Bachelor of Science, Accounting. Grand Canyon University, Master of Science, Accounting.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Dallas Fort Worth, ACT Tutors in Los Angeles, SSAT Tutors in Phoenix, Chemistry Tutors in Houston, SAT Tutors in Houston, ISEE Tutors in Los Angeles, SAT Tutors in Chicago, Physics Tutors in Seattle, Spanish Tutors in San Francisco-Bay Area, Reading Tutors in Miami

Popular Courses & Classes

LSAT Courses & Classes in Denver, SAT Courses & Classes in New York City, GRE Courses & Classes in Seattle, GMAT Courses & Classes in Houston, MCAT Courses & Classes in Philadelphia, GRE Courses & Classes in Chicago, SSAT Courses & Classes in Chicago, ACT Courses & Classes in Boston, GRE Courses & Classes in New York City, MCAT Courses & Classes in Chicago

Popular Test Prep

SSAT Test Prep in Chicago, LSAT Test Prep in Philadelphia, ACT Test Prep in Seattle, LSAT Test Prep in Phoenix, ISEE Test Prep in Los Angeles, SAT Test Prep in Dallas Fort Worth, ACT Test Prep in San Francisco-Bay Area, ISEE Test Prep in San Francisco-Bay Area, GRE Test Prep in Atlanta, SSAT Test Prep in Denver

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

High School Math : Pre-Calculus

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : Sequences And Series

Example Question #2 : Sequences And Series

Example Question #1 : Sequences And Series

Example Question #1 : Sequences And Series

Example Question #1 : Sequences And Series

Example Question #2 : Using Sigma Notation

Example Question #1 : Using Sigma Notation

Example Question #11 : Sequences And Series

Example Question #12 : Sequences And Series

Example Question #1 : Finding Terms In A Series

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: