Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : High School Math

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 : 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 #1 : Terms In A 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 #31 : Pre Calculus

What are the first three terms in the series?

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

Possible Answers:

(3)+(7)+(11)

(1)+(3)+(7)

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

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

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

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

Example Question #41 : Pre Calculus

Indicate the first three terms of the following series:

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

Possible Answers:

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

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

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

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

(1)+(5)+(9)

Correct answer:

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

Explanation:

In the arithmetic series, the first terms can be found by plugging , , and into the equation.

x=1

4(1)-5 = -1

x=2

4(2)-5 = 3

x=3

4(3)-5 = 7

Report an Error

Example Question #2051 : High School Math

Indicate the first three terms of the following series:

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

Possible Answers:

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

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

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

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

(7)+(12)+(17)

Correct answer:

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

Explanation:

In the arithmetic series, the first terms can be found by plugging in , , and for .

c=3

8-5(3) = -7

c=4

8-5(4) = -12

c=5

8-5(5) = -17

Report an Error

Example Question #3 : Finding Terms In A Series

Indicate the first three terms of the following series:

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

Possible Answers:

$(-\frac{1}{4})+(-\frac{1}{2})+(1)$

$(\frac{1}{4})+(\frac{1}{2})+(0)$

(4)+(2)+(1)

$(-\frac{1}{4})+(-\frac{1}{2})+(-1)$

$(\frac{1}{4})+(\frac{1}{2})+(1)$

Correct answer:

$(\frac{1}{4})+(\frac{1}{2})+(1)$

Explanation:

The first terms can be found by substituting , , and for into the sum formula.

m=-2

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

m=-1

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

m=0

$(2)^{0}=1$

Report an Error

Example Question #4 : Finding Terms In A Series

Indicate the first three terms of the following series.

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

Possible Answers:

$\frac{1}{2}\cdot 2\cdot 8$

Not enough information

$\frac{1}{4}\cdot 4\cdot 16$

$\frac{1}{2}+2+8$

$\frac{1}{4}+4+16$

Correct answer:

$\frac{1}{2}+2+8$

Explanation:

The first terms can be found by substituting , , and in for .

b=2

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

b=3

$\frac{1}{2}(4)^{3-2}=2$

b=4

$\frac{1}{2}(4)^{4-2}=8$

Report an Error

Example Question #1 : Finding Terms In A Series

What is the sixth term when $\left (\frac{1}{2}x-2 \right )^{10}$ is expanded?

Possible Answers:

-840x^5

-840x^6

252x^5

840x^6

-252x^5

Correct answer:

-252x^5

Explanation:

We will need to use the Binomial Theorem in order to solve this problem. Consider the expansion of (a+b)^n , where n is an integer. The rth term of this expansion is given by the following formula:

$\binom{n}{r-1}a^{n-r+1}b^{r-1}$ ,

where $\binom{n}{r-1}$ is a combination. In general, if x and y are nonnegative integers such that x > y, then the combination of x and y is defined as follows: $\binom{x}{y}=_xC_y=\frac{x!}{(y)!(x-y)!}$ .

We are asked to find the sixth term of $\left (\frac{1}{2}x-2 \right )^{10}$ , which means that in this case r = 6 and n = 10. Also, we will let $a=\frac{1}{2}x$ and b=-2 . We can now apply the Binomial Theorem to determine the sixth term, which is as follows:

$\binom{10}{6-1}\left (\frac{1}{2}x \right )^{10-6+1}\cdot(-2) ^{6-1}$

$=\binom{10}{5}\left (\frac{1}{2}x \right )^{5}\cdot(-2) ^{5}$

Next, let's find the value of $\binom{10}{5}$ . According to the definition of a combination,

$\binom{10}{5}=\frac{10!}{5!5!}=\frac{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5!}{5!5!}$

$=\frac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2}=252$ .

Remember that, if n is a positive integer, then $n!=n\cdot(n-1)\cdot(n-2)\cdot\cdot\cdot3\cdot2\cdot1$ . This is called a factorial.

Let's go back to simplifying $\binom{10}{5}\left (\frac{1}{2}x \right )^{5}\cdot(-2) ^{5}$ .

$\binom{10}{5}\left (\frac{1}{2}x \right )^{5}\cdot(-2) ^{5}=252\cdot\left (\frac{1}{2}x \right )^{5}\cdot-32$

$=252\cdot\left (\frac{1}{2} \right )^5\cdot x^5\cdot (-32) =252\cdot \frac{1}{32}\cdot-3 2\cdot x^5$

=-252x^5

The answer is -252x^5 .

Report an Error

View Tutors

Stephanie
Certified Tutor

University of West Alabama, Masters in Education, Special Education.

View Tutors

John
Certified Tutor

Arizona State University, Bachelor of Science, Microbiology.

View Tutors

Simon
Certified Tutor

University of Cambridge, Bachelor in Arts, General Literature. University of Wolverhampton, Doctor of Philosophy, History.

All High School Math Resources

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

Popular Subjects

Calculus Tutors in Washington DC, Computer Science Tutors in San Diego, Chemistry Tutors in Washington DC, Spanish Tutors in Los Angeles, Spanish Tutors in Houston, Chemistry Tutors in Dallas Fort Worth, MCAT Tutors in Washington DC, Biology Tutors in Miami, Chemistry Tutors in Boston, Biology Tutors in New York City

Popular Courses & Classes

SSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in Denver, ACT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Denver, MCAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in Miami, SAT Courses & Classes in Boston, LSAT Courses & Classes in Chicago

Popular Test Prep

SAT Test Prep in New York City, ISEE Test Prep in San Diego, GRE Test Prep in Philadelphia, GRE Test Prep in New York City, GMAT Test Prep in Philadelphia, ISEE Test Prep in Miami, GMAT Test Prep in San Diego, MCAT Test Prep in Washington DC, SSAT Test Prep in Miami, GRE Test Prep in Miami

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 : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : Using Sigma Notation

Example Question #1 : Using Sigma Notation

Example Question #1 : Terms In A Series

Example Question #31 : Pre Calculus

Example Question #1 : Finding Terms In A Series

Example Question #41 : Pre Calculus

Example Question #2051 : High School Math

Example Question #3 : Finding Terms In A Series

Example Question #4 : Finding Terms In A 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: