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 #22 : Pre Calculus

$\textup{Which of the following expressions is equivalent to }\sqrt{\frac{x^{4}y^{11}z^{5}}{x^{2}y^{5}z^{7}}} \textup{ ?}$

Possible Answers:

$\frac{xy^{3}}{z^{2}}$

$\textup{None of the other answers}$

$\frac{x^{2}y^{3}}{x^{2}}$

$\frac{xy^{3}}{z}$

$\frac{xy^{4}}{z}$

Correct answer:

$\frac{xy^{3}}{z}$

Explanation:

$\textup{Reduce the fraction by subtracting exponents, then halve all exponents to find the square root.}$

$\sqrt{\frac{x^{4}y^{11}z^{5}}{x^{2}y^{5}z^{7}}} =\sqrt{\frac{x^{2}y^{6}}{z^{2}}}\:\:=\frac{xy^{3}}{z}$

Report an Error

Example Question #1 : Sequences And Series

Evaluate: $1 - \frac{2}{3} + \frac{4}{9} - \frac{8}{27} + ...$

Possible Answers:

$\frac{2}{5}$

None of the other answers are correct.

$\frac{3}{5}$

$\frac{5}{3}$

Correct answer:

$\frac{3}{5}$

Explanation:

This sum can be determined using the formula for the sum of an infinite geometric series, with initial term $a_{0} = 1$ and common ratio $r = -\frac{2}{3}$ :

$S = \frac{a_{0}} {1-r} = \frac{1} {1- \left ( -\frac{2}{3}\right ) } = \frac{1} {1+ \frac{2}{3} }= \frac{1} { \frac{5}{3} } =\frac{3}{5}$

Report an Error

Example Question #1 : Sequences And Series

The fourth term in an arithmetic sequence is -20, and the eighth term is -10. What is the hundredth term in the sequence?

Possible Answers:

220

105

110

210

Correct answer:

220

Explanation:

An arithmetic sequence is one in which there is a common difference between consecutive terms. For example, the sequence {2, 5, 8, 11} is an arithmetic sequence, because each term can be found by adding three to the term before it.

Let $a_{n}$ denote the nth term of the sequence. Then the following formula can be used for arithmetic sequences in general:

a_n=a_1 +(n-1)d , where d is the common difference between two consecutive terms.

We are given the 4th and 8th terms in the sequence, so we can write the following equations:

a_4=a_1+(4-1)d=a_1+3d=-20

a_8=a_1+(8-1)d=a_1+7d=-10 .

We now have a system of two equations with two unknowns:

a_1+3d=-20

a_1+7d=-10

Let us solve this system by subtracting the equation a_1+7d=-10 from the equation a_1+3d=-20 . The result of this subtraction is

-4d=-10 .

This means that d = 2.5.

Using the equation a_1+7d=-10 , we can find the first term of the sequence.

a_1+7(2.5)=-10

a_1=-27.5

Ultimately, we are asked to find the hundredth term of the sequence.

$a_{100}=a_1+(100-1)d=-27.5+99(2.5)=220$

The answer is 220.

Report an Error

Example Question #1 : Sequences And Series

Find the sum, if possible:

$3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...$

Possible Answers:

$\frac{9}{2}$

$\frac{3}{2}$

Correct answer:

$\frac{9}{2}$

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. The key here is finding the rate, or pattern, between the terms. Because this is a geometric sequence, the rate is the constant by which each new term is multiplied.

Plugging in our values, we get:

$S = \frac{3}{1-\frac{1}{3}}$

$S=\frac{3}{\frac{2}{3}}$

$S = \frac{9}{2}$

Report an Error

Example Question #2 : Sequences And Series

Find the sum, if possible:

$8-6+\frac{9}{2}-\frac{27}{8}+...$

Possible Answers:

$\frac{34}{7}$

$\frac{30}{7}$

$\frac{26}{7}$

$\frac{32}{7}$

$\frac{28}{7}$

Correct answer:

$\frac{32}{7}$

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

Because the terms switch sign, we know that the rate must be negative.

Plugging in our values, we get:

$S = \frac{8}{1-(\frac{-3}{4})}$

$S = \frac{8}{\frac{7}{4}}$

$S = \frac{32}{7}$

Report an Error

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 #31 : Pre Calculus

Determine the summation notation for the following series:

3+9+27+81+243

Possible Answers:

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

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

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

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

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

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:

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

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

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

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

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

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

View Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

View Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

View Tutors

Robert
Certified Tutor

University of Pittsburgh, Bachelor of Science, Physics.

All High School Math Resources

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

Popular Subjects

LSAT Tutors in New York City, Computer Science Tutors in Atlanta, GRE Tutors in Boston, SSAT Tutors in Miami, English Tutors in Chicago, ACT Tutors in Dallas Fort Worth, Algebra Tutors in Los Angeles, Calculus Tutors in Atlanta, GRE Tutors in Seattle, French Tutors in Washington DC

Popular Courses & Classes

SSAT Courses & Classes in Seattle, SSAT Courses & Classes in Atlanta, SSAT Courses & Classes in Phoenix, SSAT Courses & Classes in San Diego, MCAT Courses & Classes in Boston, ISEE Courses & Classes in Denver, GRE Courses & Classes in Boston, SSAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Philadelphia

Popular Test Prep

GRE Test Prep in Boston, ISEE Test Prep in Denver, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Atlanta, GRE Test Prep in Denver, ISEE Test Prep in Philadelphia, ISEE Test Prep in Phoenix, GRE Test Prep in Philadelphia, MCAT Test Prep in New York City

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 #22 : Pre Calculus

Example Question #1 : Sequences And Series

Example Question #1 : Sequences And Series

Example Question #1 : Sequences And Series

Example Question #2 : Sequences And Series

Example Question #2 : Sequences And Series

Example Question #31 : Pre Calculus

Example Question #1 : Sequences And Series

Example Question #1 : Sequences And Series

Example Question #1 : Sequences And Series

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: