We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Common Difference in Sequences

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Sequences

In the sequence 3, ____, ____, 24, what numbers can fill the two blanks so that consecutive terms differ by a common ratio?

Possible Answers:

10, 15

12, 16

9, 18

6, 12

10, 17

Correct answer:

6, 12

Explanation:

If the common ratio is r, then the sequence can be rewritten as 3, 3r, , . We see then that , which gives us that r=2. Therefore, the missing terms are 6 and 12.

Report an Error

Example Question #3 : Sequences

Find the common difference of the following sequence:

$\displaystyle 4, 9, 14,19,24,29,...$

Possible Answers:

$\displaystyle 10$

$\displaystyle 5$

$\displaystyle 6$

$\displaystyle 3$

Correct answer:

$\displaystyle 5$

Explanation:

The common difference is equal to

$a_{n+1}\:-\:a_{n}$ $\displaystyle a_{n+1}\:-\:a_{n}$

Plugging our values into this equation we can find the common difference.

9-4=5 $\displaystyle 9-4=5$

14-9=5 $\displaystyle 14-9=5$

$\vdots$ $\displaystyle \vdots$

Therefore, in this case the common difference is $\displaystyle 5$.

Report an Error

Example Question #1 : Common Difference In Sequences

Find the common difference of the following sequence:

$\displaystyle 1,4,7,10,13,16,19,22,25,28,...$

Possible Answers:

$\displaystyle 4$

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 2$

Correct answer:

$\displaystyle 3$

Explanation:

The common difference is equal to

$a_{n+1}\:-\:a_{n}$ $\displaystyle a_{n+1}\:-\:a_{n}$.

Plugging in the values from this problem we get,

4-1=3 $\displaystyle 4-1=3$

7-4=3 $\displaystyle 7-4=3$

$\vdots$ $\displaystyle \vdots$

Therefore, in this case the common difference is $\displaystyle 3$.

Report an Error

Example Question #1 : How To Find The Common Difference In Sequences

Find the common difference of the following sequence:

$\displaystyle 2,4,6,8,10,12,...$

Possible Answers:

$\displaystyle 2$

$\displaystyle 1$

$\displaystyle 4$

$\displaystyle 3$

Correct answer:

$\displaystyle 2$

Explanation:

The common difference is equal to

$a_{n+1}\:-\:a_{n}$ $\displaystyle a_{n+1}\:-\:a_{n}$.

Plugging in the values from this problem we get,

4-2=2 $\displaystyle 4-2=2$

6-4=2 $\displaystyle 6-4=2$

$\vdots$ $\displaystyle \vdots$

Therefore, in this case the common difference is $\displaystyle 2$.

Report an Error

Example Question #1 : How To Find The Common Difference In Sequences

The following is an arithmetic sequence. Find an explicit equation for it in terms of the common difference.

${\large} 3, 7, 11, 15, 19,...{}$ $\displaystyle {\large} 3, 7, 11, 15, 19,...{}$

Possible Answers:

${\large} a_n=3n+1$ $\displaystyle {\large} a_n=3n+1$

${\large} a_n=4n+2$ $\displaystyle {\large} a_n=4n+2$

${\large} a_n = 4n-1$ $\displaystyle {\large} a_n = 4n-1$

${\large} a_n=3n$ $\displaystyle {\large} a_n=3n$

Correct answer:

${\large} a_n = 4n-1$ $\displaystyle {\large} a_n = 4n-1$

Explanation:

Finding the common difference is fairly simple. We simply subtract the first term from the second. 7-3 = 4, so 4 is our common difference. So each term is going to be 4n plus something:

${\large} a_n = 4n+x$ $\displaystyle {\large} a_n = 4n+x$

We know the first term is 3, so we can plug in that to our equation.

${\large} 3=4+x$ $\displaystyle {\large} 3=4+x$

$\large x=-1$ $\displaystyle \large x=-1$

So the explicit form of our arithmetic sequence is

${\large} a_n=4n-1$ $\displaystyle {\large} a_n=4n-1$.

Report an Error

View ACT Math Tutors

Anatole
Certified Tutor

CUNY Hunter College, Bachelor in Arts, Multimedia.

View ACT Math Tutors

Anabel
Certified Tutor

UDELAR, Diploma, Chemistry. IPA, Bachelor of Education, Mathematics.

View ACT Math Tutors

Cole
Certified Tutor

UW Madison, Bachelors, Industrial Engineering. UW Madison, Masters, Industrial Engineering.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Atlanta, MCAT Courses & Classes in Miami, Spanish Courses & Classes in Atlanta, GMAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Denver, GMAT Courses & Classes in Chicago, LSAT Courses & Classes in San Diego, GRE Courses & Classes in Los Angeles, ISEE Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Atlanta, GRE Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in Los Angeles, LSAT Test Prep in Philadelphia, GRE Test Prep in Miami, MCAT Test Prep in Miami, MCAT Test Prep in Los Angeles, SSAT Test Prep in Chicago

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

ACT Math : Common Difference in Sequences

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Sequences

Example Question #3 : Sequences

Example Question #1 : Common Difference In Sequences

Example Question #1 : How To Find The Common Difference In Sequences

Example Question #1 : How To Find The Common Difference In Sequences

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: