Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : Arithmetic Sequences

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : How To Find The Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

$1 \frac{1}{7}, 3 \frac{1}{4},...$

Which of the following is the first term greater than 100?

Possible Answers:

The forty-ninth term

The fifty-first term

The fiftieth term

The forty-eighth term

The forty-seventh term

Correct answer:

The forty-eighth term

Explanation:

The common difference of the sequence is

$3 \frac{1}{4} - 1 \frac{1}{7} = 2\frac{3}{28}$

so the th term of the sequence is

$a_{n} = 1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) (n-1)$

To find out the minimum value for which $a_{n} > 100$ , set up this inequality:

$1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) (n-1) > 100$

$1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) n -2\frac{3}{28} > 100$

$\left ( 2\frac{3}{28} \right ) n - \frac{27}{28} > 100$

$\left ( 2\frac{3}{28} \right ) n > 100 \frac{27}{28}$

$n > 100 \frac{27}{28} \div 2\frac{3}{28} = 47 \frac{54}{59}$

The correct response is the forty-eighth term.

Report an Error

Example Question #3 : How To Find The Nth Term Of An Arithmetic Sequence

The tenth and twelfth terms of an arithmetic sequence are 8.4 and 10.2. What is its first term?

Possible Answers:

0.9

1.2

1.8

0.3

-0.6

Correct answer:

0.3

Explanation:

The th term of an arithmetic sequence with initial term $a_{1}$ and common difference is defined by the equation

$a_{n} = a_{1}+ (n-1)d$

Since the tenth and twelfth terms are two terms apart, the common difference can be found as follows:

$a_{10}+2d=a_{12}$

8.4+2d=10.2

8.4+2d- 8.4=10.2 - 8.4

2d=1.8

d = 0.9

Now, we can set n = 10, d = 0.9 in the sequence equation to find $a_{1}$ :

$a_{n} = a_{1}+ (n-1)d$

$a_{10} = a_{1}+ (10-1)0.9$

$8.4 = a_{1}+ 9 \cdot 0.9$

$8.4 = a_{1}+ 8.1$

$8.4 - 8.1 = a_{1}+ 8.1 - 8.1$

$a_{1} = 0.3$

Report an Error

Example Question #6 : How To Find The Nth Term Of An Arithmetic Sequence

The eleventh and thirteenth terms of an arithmetic sequence are, respectively, 11 and 14. Give its first term.

Possible Answers:

$1\frac{1}{2}$

$-5\frac{1}{2}$

$-2\frac{1}{2}$

Correct answer:

Explanation:

The th term of an arithmetic sequence with initial term $a_{1}$ and common difference is defined by the equation

$a_{n} = a_{1}+ (n-1)d$

Since the eleventh and thirteenth terms are two terms apart, the common difference can be found as follows:

$a_{11}+2d=a_{13}$

11+2d=14

11+2d -11=14 -11

2d = 3

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

Now, we can set $n = 11, d =\frac{3}{2}$ in the sequence equation to find $a_{1}$ :

$a_{11} = a_{1}+ (11-1) \frac{3}{2}$

$11= a_{1}+ 10 \cdot \frac{3}{2}$

$11= a_{1}+ 15$

$11- 15= a_{1}+ 15 - 15$

$a_{1} = -4$

Report an Error

Example Question #42 : Sequences And Series

The lengths of the sides of ten squares form an arithmetic sequence. One side of the smallest square measures eight inches; one side of the second-smallest square measures one foot.

Give the area of the largest square.

Possible Answers:

576 square inches

1,936 square inches

484 square inches

784 square inches

2,304 square inches

Correct answer:

1,936 square inches

Explanation:

Let $a_{n}$ be the lengths of the sides of the squares in inches. $a_{1} = 8$ and $a_{2} = 12$ , so their common difference is

$d = a_{2} - a_{1} = 12 - 8 = 4$

The arithmetic sequence formula is

$a_{n} = a_{1} + (n-1)d$

The length of a side of the largest square - square 10 - can be found by substituting $a_{1} = 8, n= 10, d = 4$ :

$a_{10} =8+ (10-1) 4 = 8 + 9 \cdot 4 = 8 + 36 = 44$

The largest square has sides of length 44 inches, so its area is the square of this, or $A = 44^{2} = 1,936$ square inches.

Report an Error

Example Question #11 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

12, 19, 26, 33,...

Give the thirty-second term of this sequence.

Possible Answers:

250

229

243

236

222

Correct answer:

229

Explanation:

The th term of an arithmetic sequence with initial term $a_{1}$ and common difference is defined by the equation

$a_{n} = a_{1}+ (n-1)d$

The initial term in the given sequence is

$a_{1} = 12$ ;

the common difference is

d = 19-12= 7 ;

We are seeking term n = 32 .

This term is

$a_{32} = 12+ (32-1) 7$

$a_{32} = 12+ 31 \cdot 7 = 12+ 217 = 229$

Report an Error

Example Question #541 : Number Concepts And Operations

An arithmetic sequence begins as follows:

$\frac{2}{5} , \frac{7}{10}, 1, 1 \frac{3}{10}, ...$

Give the thirty-third term of this sequence.

Possible Answers:

$9\frac{9}{10}$

$10\frac{1}{10}$

$9\frac{4}{5}$

$10 \frac{1}{5}$

The correct answer is not given among the other four responses.

Correct answer:

The correct answer is not given among the other four responses.

Explanation:

The th term of an arithmetic sequence with initial term $a_{1}$ and common difference is defined by the equation

$a_{n} = a_{1}+ (n-1)d$ .

The initial term in the given sequence is

$a_{1} = \frac{2}{5}$ ;

the common difference is

$d = \frac{7}{10} - \frac{2}{5} = \frac{7}{10} - \frac{4}{10} = \frac{3}{10}$ .

We are seeking term n = 33 .

Therefore,

$a_{33} = \frac{2}{5}+ (33-1) \frac{3}{10}$

$= \frac{2}{5}+ (32) \frac{3}{10}$

$= \frac{2}{5}+ \frac{96}{10}$

$= \frac{2}{5}+ \frac{48}{5}$

$= \frac{50}{5} = 10$ ,

which is not among the choices.

Report an Error

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

What is the value of x in the sequence below?

99, 33, 11, x

Possible Answers:

$\frac{11}{2}$

$11\frac{1}{3}$

$3\frac{2}{3}$

Correct answer:

$3\frac{2}{3}$

Explanation:

In this sequence, each subsequent number is equal to one third of the preceding number.

One third of 11 is equal to:

$\frac{11}{3}=3\frac{2}{3}$

Therefore, the correct answer is: $3\frac{2}{3}$

Report an Error

Example Question #2 : How To Find The Next Term In An Arithmetic Sequence

Find the next term of the arithmetic sequence:

24, 29, 34, ?

Possible Answers:

Correct answer:

Explanation:

The common difference for this sequence is . To find the next number in the sequence, add to the last given number.

34+5=39

Report an Error

Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

Find the next term of this arithmetic sequence:

-15, -8, -1, ?

Possible Answers:

Correct answer:

Explanation:

The common difference for this sequence is . Add this to the last given term to find the next one.

-1+7=6

Report an Error

Example Question #544 : Number Concepts And Operations

Find the next term of the arithmetic sequence:

-4, 5, 14, ?

Possible Answers:

Correct answer:

Explanation:

The common difference is . Add this to the last given term to find the next term.

14+9=23

Report an Error

View SSAT- Upper Level Tutors

Sundeep
Certified Tutor

Indian Institute of Technology, Engineering in Computer Science, Electrical Engineering. New York University, Masters in Busi...

View SSAT- Upper Level Tutors

Colin
Certified Tutor

Cooper Union for the Advancement of Science and Art, Bachelor of Fine Arts, Fine and Studio Arts Management. The University o...

View SSAT- Upper Level Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Philadelphia, MCAT Tutors in Miami, Biology Tutors in Dallas Fort Worth, LSAT Tutors in New York City, Biology Tutors in Washington DC, Statistics Tutors in San Diego, French Tutors in Philadelphia, GRE Tutors in Chicago, GRE Tutors in Atlanta, Physics Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Phoenix, SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Seattle, SSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Los Angeles, MCAT Courses & Classes in Boston, SSAT Courses & Classes in Washington DC, GMAT Courses & Classes in San Diego, MCAT Courses & Classes in Los Angeles

Popular Test Prep

SAT Test Prep in Denver, GMAT Test Prep in Atlanta, MCAT Test Prep in Phoenix, GMAT Test Prep in San Diego, LSAT Test Prep in Washington DC, GMAT Test Prep in Chicago, MCAT Test Prep in Atlanta, SSAT Test Prep in New York City, LSAT Test Prep in Seattle, ACT 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

SSAT Upper Level Math : Arithmetic Sequences

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #4 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #3 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #6 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #42 : Sequences And Series

Example Question #11 : Nth Term Of An Arithmetic Sequence

Example Question #541 : Number Concepts And Operations

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Example Question #2 : How To Find The Next Term In An Arithmetic Sequence

Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

Example Question #544 : Number Concepts And Operations

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: