Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math I : Sequences

Study concepts, example questions & explanations for SAT II Math I

Create An Account

All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #61 : Mathematical Relationships

The first and third terms of a geometric sequence comprising only positive elements are $\sqrt{20}$ and $\sqrt{180}$ , respectively. In simplest form, which of the following is its second term?

Possible Answers:

$6 \sqrt{5}$

$2 \sqrt{15}$

$4 \sqrt{10}$

None of these

Correct answer:

$2 \sqrt{15}$

Explanation:

Let be the common ratio of the geometric sequence. Then

$a_{2} = r a_{1}$

and

$a_{3} = r a_{2}= r \cdot r a_{1} = r ^{2}a_{1}$

Therefore,

$r ^{2} = \frac{a_{3}}{a_{1}}$ ,

Setting $a_{1}= \sqrt{20}, a_{3} = \sqrt{180}$ , and applying the Quotient of Radicals Rule:

$r ^{2} = \frac{a_{3}}{a_{1}} = \frac{\sqrt{180}}{\sqrt{20}} = \sqrt{9} = 3$

Taking the square root of both sides:

$r = \pm \sqrt{3}$

Substituting, and applying the Product of Radicals Rule:

$a_{2} = r a_{1}$

$a_{2} = \pm \sqrt{3} \cdot \sqrt{20 } =\pm \sqrt{60 } = \pm \sqrt{4} \cdot \sqrt{15}= \pm 2 \sqrt{15}$

Since all elements of the sequence are positive, $a_{2} = 2 \sqrt{15}$ .

Report an Error

View SAT Subject Test in Mathematics Level 1 Tutors

Reuben
Certified Tutor

University of Alberta, Bachelor of Science, Mathematics.

View SAT Subject Test in Mathematics Level 1 Tutors

Peter
Certified Tutor

Nottingham University UK, Bachelor in Arts, Mathematics.

View SAT Subject Test in Mathematics Level 1 Tutors

Maggie
Certified Tutor

New York University, Bachelor of Science, Digital Communications and Multimedia.

All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in San Diego, Biology Tutors in Chicago, Chemistry Tutors in New York City, SSAT Tutors in Seattle, Spanish Tutors in Washington DC, Calculus Tutors in San Francisco-Bay Area, French Tutors in New York City, Math Tutors in San Diego, SSAT Tutors in Los Angeles, Math Tutors in Atlanta

Popular Courses & Classes

SSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, MCAT Courses & Classes in Boston, LSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Denver, ISEE Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Washington DC, SAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Philadelphia

Popular Test Prep

GMAT Test Prep in Chicago, SAT Test Prep in Phoenix, GRE Test Prep in Philadelphia, MCAT Test Prep in Atlanta, ACT Test Prep in Phoenix, MCAT Test Prep in Phoenix, SAT Test Prep in Washington DC, ISEE Test Prep in Miami, GMAT Test Prep in New York City, GMAT Test Prep in Washington DC

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

SAT II Math I : Sequences

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #61 : Mathematical Relationships

All SAT II Math I Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: