Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Summations and Sequences

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Summations And Sequences

Which of the following is a geometric sequence?

Possible Answers:

$t_{0}=4$

$t_{n}=t_{n-1}\times 3$

$t_{0}=5$

$t_{n}=t_{n-1}+3$

$t_{0}=2$

$t_{n} = t_{n-1}^{6}$

$t_{0}=4$

$t_{n}=t_{n-1}+3.4$

$t_{0}=10$

$t_{n}=t_{n-1}+5$

Correct answer:

$t_{0}=4$

$t_{n}=t_{n-1}\times 3$

Explanation:

A geometric sequence is one in which the next term is found by mutlplying the previous term by a particular constant. Thus, we look for an implicit definition which involves multiplication of the previous term. The only possibility is:

$t_{0}=4$

$t_{n}=t_{n-1}\times 3$

Report an Error

Example Question #1 : Geometric Sequences

$\left \{ -1, 2, -4, 8, -16, 32... \right \}$

What is the explicit formula for the above sequence? What is the 20th value?

Possible Answers:

$a_{n}=a_{1}\cdot-2;\ a_{20}=-524288$

$a_{n}= -1\cdot -2^{n-1};\ a_{20} = 524288$

$a_{n}=a_{n-1}\cdot-2^{n-1};\ a_{20} = -262144$

$a_{n}=a_{n-1}\cdot-1;\ a_{20}=524288$

$a_{n-1}= a_{n}\cdot -2;\ a_{20}=-524288$

Correct answer:

$a_{n}= -1\cdot -2^{n-1};\ a_{20} = 524288$

Explanation:

This is a geometric series. The explicit formula for any geometric series is:

$a_{n}= a_{1} \cdot r^{n-1}$ , where is the common ratio and is the number of terms.

In this instance r = -2 and a_1=-1 .

$a_{n}= a_{1} \cdot r^{n-1}\rightarrow a_n=(-1)\cdot(-2)^{n-1}$

Substitute n = 20 into the equation to find the 20th term:

$a_{20}=(-1)\cdot(-2)^{20-1}$

$a_{20}=-(-2)^{19}=-(-524288)=524288$

Report an Error

Example Question #1 : Summations And Sequences

What type of sequence is shown below?

$\left \{ 4,9,15,22,30... \right \}$

Possible Answers:

Subtractive

Geometric

None of the other answers

Arithmetic

Multiplicative

Correct answer:

None of the other answers

Explanation:

This series is neither geometric nor arithmetic.

A geometric sequences is multiplied by a common ratio () each term. An arithmetic series adds the same additional amount () to each term. This series does neither.

Mutiplicative and subtractive are not types of sequences.

Therefore, the answer is none of the other answers.

Report an Error

Example Question #2 : Mathematical Relationships And Basic Graphs

Identify the 10th term in the series:

$\left \{ \frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32}... \right \}$

Possible Answers:

$\frac{1}{8192}$

$\frac{1}{2048}$

$\frac{1}{512}$

$\frac{1}{1634}$

$\frac{1}{4096}$

Correct answer:

$\frac{1}{2048}$

Explanation:

The explicit formula for a geometric series is $a_{n}=a_{1}\cdot r^{n-1}$

In this problem $r=\frac{1}{2}$

Therefore:

$a_{10}=\frac{1}{4}\cdot \frac{1}{2}^{9}$

${\color{Red} a_{10}=\frac{1}{2048}}$

Report an Error

Example Question #1 : Geometric Sequences

Which of the following could be the formula for a geometric sequence?

Possible Answers:

$a_6=3\cdot 7^5, a_1=3$

a_4=a_3+9(n+1)

a_3=6+4(n-1)

$a_4=5\cdot (\frac{1}{3})^4$

$a_{16}=a_{15}\cdot 3$

Correct answer:

$a_6=3\cdot 7^5, a_1=3$

Explanation:

The explicit formula for a geometric series is $a_n=a_1\cdot r^{n-1}$ .

Therefore, ${\color{Red} a_6=3\cdot 7^5, a_1=3}$ is the only answer that works.

Report an Error

Example Question #1 : Mathematical Relationships And Basic Graphs

Find the 15th term of the following series:

$\left \{ 120, 60, 30, 15, 7.5,... \right \}$

Possible Answers:

$a_{15}=.0016$

$a_{15}=.0025$

$a_{15}=.0018$

$a_{15}=.0037$

$a_{15}=.0073$

Correct answer:

$a_{15}=.0073$

Explanation:

This series is geometric. The explicit formula for any geometric series is:

$a_n=a_1\cdot r^{n-1}$

Where represents the $n^{th}$ term, a_1 is the first term, and is the common ratio.

In this series $r = \frac{1}{2}$ .

Therefore the formula to find the 15th term is:

$a_{15}=120\cdot \left(\frac{1}{2}\right)^{14}$

$a_{15}=.0073$

Report an Error

Example Question #1 : How To Find The Missing Number In A Set

2, 6, 18, n, 162...

$\textup{In the above geometric sequence, what is the value of }n\textup{?}$

Possible Answers:

Correct answer:

Explanation:

$\textup{Look for a pattern. Each term in the sequence is three times the previous term.}$

$18\ast3=54$

Report an Error

Example Question #7 : Mathematical Relationships And Basic Graphs

Give the 33rd term of the Geometric Series

2, -3, 4.5, -6.75, ...

[2 is the first term]

Possible Answers:

431,439. 884

-1,294,319.650

1,853,020,188, 851, 841

862,879.767

12,987

Correct answer:

862,879.767

Explanation:

First we need to find the common ratio by dividing the second term by the first:

$-3 \div 2 = -1.5$

The $n^{th}$ term is

$\\a_{n} = a_1(r)^{n-1}\\a_n=2(-1.5)^{n-1}$ ,

so the 33rd term will be

$a_{33} = 2(-1.5)^ {32 } = 862,879.767$ .

Report an Error

Example Question #6 : Mathematical Relationships And Basic Graphs

Find the 19th term of the sequence $7,000, \enspace 2,800, \enspace 1,120, \enspace 448, ...$

[the first term is 7,000]

Possible Answers:

0.000481

1.119

14,551, 915.228

0.000192

0.00000000184

Correct answer:

0.000481

Explanation:

First find the common ratio by dividing the second term by the first:

$2,800 \div 7,000 = \frac{ 2}{5} = 0.4$

Since the first term is 7,000 , the nth term can be found using the formula

$\\a_{n} = a_1(r)^{n-1}$

$7,000(0.4)^ {n-1 }$ ,

so the 19th term is $7,000(0.4)^{18} = 0.000481$

Report an Error

Example Question #9 : Mathematical Relationships And Basic Graphs

Find the 21st term of the sequence 90, 108, 129.6, 155.52, ...

[90 is 1st, so n=1]

Possible Answers:

2.348

55.206

3,450.384

1.956

4,140.461

Correct answer:

3,450.384

Explanation:

First, find the common ratio by dividing the second term by the first:

$108 \div 90 = 1.2$

The nth term can be found using

$\\a_{n} = a_1(r)^{n-1}$

$90(1.2)^ {n-1}$ ,

so the 21st term is

$90(1.2) ^ {20 } = 3,450.384$ .

Report an Error

View Algebra 2 Tutors

Lilian Natalia
Certified Tutor

University of Texas Rio Grande Valley, Bachelor of Science, Mechanical Engineering. University of Texas Rio Grande Valley, Ma...

View Algebra 2 Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Algebra 2 Tutors

Nicholas
Certified Tutor

Salem State University, Bachelor of Science, GIS Technology.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Phoenix, Computer Science Tutors in Miami, ACT Tutors in New York City, Reading Tutors in Philadelphia, Spanish Tutors in Miami, SAT Tutors in Atlanta, Spanish Tutors in Denver, Spanish Tutors in Chicago, Calculus Tutors in Phoenix, Algebra Tutors in Houston

Popular Courses & Classes

MCAT Courses & Classes in Philadelphia, ACT Courses & Classes in Atlanta, Spanish Courses & Classes in San Diego, GMAT Courses & Classes in San Diego, SSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Miami, GMAT Courses & Classes in Denver, GMAT Courses & Classes in Seattle, GMAT Courses & Classes in Houston, ACT Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in Chicago, GMAT Test Prep in Houston, SAT Test Prep in Houston, MCAT Test Prep in Phoenix, SAT Test Prep in Atlanta, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Boston, SAT Test Prep in Miami, ISEE Test Prep in San Francisco-Bay Area, GMAT 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

Algebra II : Summations and Sequences

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Summations And Sequences

Example Question #1 : Geometric Sequences

Example Question #1 : Summations And Sequences

Example Question #2 : Mathematical Relationships And Basic Graphs

Example Question #1 : Geometric Sequences

Example Question #1 : Mathematical Relationships And Basic Graphs

Example Question #1 : How To Find The Missing Number In A Set

Example Question #7 : Mathematical Relationships And Basic Graphs

Example Question #6 : Mathematical Relationships And Basic Graphs

Example Question #9 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: