We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Functions : Write, Model, and Translate Arithmetic and Geometric Sequences Recursively and Explicitly: CCSS.Math.Content.HSF-BF.A.2

Study concepts, example questions & explanations for Common Core: High School - Functions

Create An Account

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

(1,-2,-5,-8,... )

Possible Answers:

f(n)=-1+3(n-1)

f(n)=1+3(n+1)

f(n)=1+3(n-1)

f(n)=1-3(n-1)

f(n)=1-3(n+1)

Correct answer:

f(n)=1-3(n-1)

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=-2-1 \\d=-3$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=1 \\d=-3$

Step 3: Substitute known values into the form from Step 2.

f(n)=1-3(n-1)

Report an Error

Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

(2,5,8,11,... )

Possible Answers:

f(n)=2-3(n-1)

f(n)=2+1(n-1)

f(n)=2+5(n-1)

f(n)=-2+5(n-1)

f(n)=2+3(n-1)

Correct answer:

f(n)=2+3(n-1)

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=5-2 \\d=3$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=2 \\d=3$

Step 3: Substitute known values into the form from Step 2.

f(n)=2+3(n-1)

Report an Error

Example Question #31 : Building Functions

Write an explicit recursive function that describes the following sequence.

(4,6,8,10,... )

Possible Answers:

f(n)=-4+2(n-1)

f(n)=4-2(n-1)

f(n)=2+4(n-1)

f(n)=4+2(n-1)

f(n)=4+(n-1)

Correct answer:

f(n)=4+2(n-1)

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=6-4 \\d=2$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=4 \\d=2$

Step 3: Substitute known values into the form from Step 2.

f(n)=4+2(n-1)

Report an Error

Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

(-1,-7,-13,-19,... )

Possible Answers:

f(n)=-1-8(n-1)

f(n)=1-6(n-1)

f(n)=1+6(n-1)

f(n)=-1-6(n-1)

f(n)=-1+6(n-1)

Correct answer:

f(n)=-1-6(n-1)

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=-7--1 \\d=-6$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=-1 \\d=-6$

Step 3: Substitute known values into the form from Step 2.

f(n)=-1-6(n-1)

Report an Error

Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

(3,4,5,6,... )

Possible Answers:

f(n)=3+1(n-1)

f(n)=1+3(n-1)

f(n)=3-1(n-1)

f(n)=-3+1(n-1)

f(n)=1-3(n-1)

Correct answer:

f(n)=3+1(n-1)

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=4-3 \\d=1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=3 \\d=1$

Step 3: Substitute known values into the form from Step 2.

f(n)=3+1(n-1)

Report an Error

Example Question #208 : High School: Functions

Write an explicit recursive function that describes the following sequence.

$\left(\frac{3}{4},\frac{1}{4},-\frac{1}{4},-\frac{3}{4},...\right)$

Possible Answers:

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

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

$f(n)=\frac{3}{2}-\frac{1}{2}(n-1)$

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

$f(n)=\frac{3}{4}-\frac{1}{4}(n-1)$

Correct answer:

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

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\\\d=\frac{1}{4}-\frac{3}{4} \\\\d=-\frac{1}{2}$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=\frac{3}{4} \\\\d=-\frac{1}{2}$

Step 3: Substitute known values into the form from Step 2.

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

Report an Error

Example Question #4 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

(-2,3,8,13,... )

Possible Answers:

f(n)=-2+5(n-1)

f(n)=-5+2(n-1)

f(n)=2-5(n-1)

f(n)=5+5(n-1)

f(n)=5+2(n-1)

Correct answer:

f(n)=-2+5(n-1)

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=3--2 \\d=5$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=-2 \\d=5$

Step 3: Substitute known values into the form from Step 2.

f(n)=-2+5(n-1)

Report an Error

Example Question #5 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

$\left(\frac{1}{2},\frac{3}{2},\frac{5}{2},\frac{7}{2},... \right )$

Possible Answers:

$f(n)=-\frac{1}{2}+1(n-1)$

$f(n)=\frac{1}{2}+1(n+1)$

$f(n)=\frac{1}{2}+1(n-1)$

$f(n)=\frac{1}{2}-1(n-1)$

$f(n)=1+\frac{1}{2}(n-1)$

Correct answer:

$f(n)=\frac{1}{2}+1(n-1)$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\\\d=\frac{3}{2}-\frac{1}{2} \\\\d=1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=\frac{1}{2} \\\\d=1$

Step 3: Substitute known values into the form from Step 2.

$f(n)=\frac{1}{2}+1(n-1)$

Report an Error

Example Question #6 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

(3,-1,-5,-9,... )

Possible Answers:

f(n)=3-4(n-1)

f(n)=4-3(n-1)

f(n)=3+4(n-1)

f(n)=-4+3(n-1)

f(n)=-3-4(n-1)

Correct answer:

f(n)=3-4(n-1)

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=-1-3 \\d=-4$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=3 \\d=-4$

Step 3: Substitute known values into the form from Step 2.

f(n)=3-4(n-1)

Report an Error

Example Question #5 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

(5,-5,-15,-25,... )

Possible Answers:

f(n)=-5+10(n-1)

f(n)=10-5(n-1)

f(n)=5+10(n-1)

f(n)=-5-10(n-1)

f(n)=5-10(n-1)

Correct answer:

f(n)=5-10(n-1)

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=-5-5 \\d=-10$

Step 2: Identify the basic form for an arithmetic recursive sequence.

f(n)=A+d(n-1)

where

$\\A=5 \\d=-10$

Step 3: Substitute known values into the form from Step 2.

f(n)=5-10(n-1)

Report an Error

View Tutors

Elisabeth
Certified Tutor

The Texas A&M University System Office, Bachelor of Science, Social Work. National University, Master of Science, Applied Beh...

View Tutors

Shifrah
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Biology, General. Massachusetts College of Pharmacy and Health ...

View Tutors

Grace
Certified Tutor

University of Evansville, Bachelor of Science, Archaeology.

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Atlanta, ISEE Tutors in Philadelphia, ISEE Tutors in Denver, LSAT Tutors in Philadelphia, Algebra Tutors in Seattle, GRE Tutors in Dallas Fort Worth, Spanish Tutors in Chicago, LSAT Tutors in San Diego, ISEE Tutors in Dallas Fort Worth, SSAT Tutors in Washington DC

Popular Courses & Classes

SAT Courses & Classes in Phoenix, GRE Courses & Classes in Denver, GRE Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Seattle, SAT Courses & Classes in Miami, GMAT Courses & Classes in Atlanta, ACT Courses & Classes in Phoenix, Spanish Courses & Classes in Miami, GRE Courses & Classes in New York City, Spanish Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in Denver, ISEE Test Prep in Denver, ACT Test Prep in Phoenix, SSAT Test Prep in New York City, LSAT Test Prep in Chicago, SAT Test Prep in Philadelphia, LSAT Test Prep in Boston, SSAT Test Prep in Miami, MCAT Test Prep in Los Angeles, GRE Test Prep in San Diego

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

Common Core: High School - Functions : Write, Model, and Translate Arithmetic and Geometric Sequences Recursively and Explicitly: CCSS.Math.Content.HSF-BF.A.2

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #31 : Building Functions

Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #208 : High School: Functions

Example Question #4 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #5 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #6 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #5 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

All Common Core: High School - Functions Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: