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 #11 : Arithmetic Sequences

Leon makes $\$2.00$ for the first hour of work, $\$6.00$ for his second hour of work, $\$10.00$ for his third hour of work, and so on. How much will he make for his $12^{th}$ hour of work?

Possible Answers:

$\$46$

$\$50$

$\$54$

$\$42$

Correct answer:

$\$46$

Explanation:

You should recognize this as an arithmetic sequence:

2, 6, 10...

The question is asking you to find the 12th term in this particular sequence.

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

Using the information given from the question,

a_1=2

n=12

d=4

Now, plug in the information to find the value of the 12th term.

$y_{12}=2+(12-1)(4)=2+(11)(4)=2+44=46$

Report an Error

Example Question #12 : Other Arithmetic Sequences

Find the sum of the first terms of the following arithmetic sequence:

-10, -4, 2, 8...

Possible Answers:

Correct answer:

Explanation:

To find the sum of a certain number of terms in an arithmetic sequence, use the following formula:

$\text{Sum}=\frac{n(y_1+y_n)}{2}$

the number of the terms you have
the first term of the sequence
$y_n=n^{th}$ term of the sequence

To find the sum, we need to first find the 8th term of the sequence.

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

Using the information given from the question,

a_1=-10

n=8

d=-4-(-10)=6

Now, plug in the information to find the value of the 8th term.

y_8=-10+(8-1)(6)=-10+(7)(6)=-10+42=32

Now that we know the 8th term of the sequence, we can plug in that value into the equation for the sum to find what these first 8 terms add up to.

$\text{Sum}=\frac{8(-10+32)}{2}=\frac{(8)(22)}{2}=88$

Report an Error

Example Question #13 : Other Arithmetic Sequences

Find the sum of the first terms of the following arithmetic sequence:

15, 11, 7, 3...

Possible Answers:

Correct answer:

Explanation:

To find the sum of a certain number of terms in an arithmetic sequence, use the following formula:

$\text{Sum}=\frac{n(y_1+y_n)}{2}$

the number of the terms you have
the first term of the sequence
$y_n=n^{th}$ term of the sequence

To find the sum, we need to first find the 9th term of the sequence.

To find any term in an arithmetic sequence, use the following formula:

y_n=a_1+(n-1)d

is the term we want to find
is the first term of the sequence
is the number of the term we want to find
is the common difference

Using the information given from the question,

a_1=15

n=9

d=11-15=-4

Now, plug in the information to find the value of the 9th term.

y_9=15+(9-1)(-4)=15+(8)(-4)=15+(-32)=17

Now that we know the 9th term of the sequence, we can plug in that value into the equation for the sum to find what these first 9 terms add up to.

$\text{Sum}=\frac{9(15+(-17))}{2}=\frac{(9)(-2)}{2}=-9$

Report an Error

Example Question #11 : Arithmetic Sequences

The first two terms of an arithmetic sequence are 1,000 and 997, in that order. What is the seventieth term?

Possible Answers:

796

1,207

790

793

1,210

Correct answer:

793

Explanation:

The first term is $x_{0} = 1,000$ .

The common difference is

997 - 1,000 = -3 .

The seventieth term is

$x_{69} = x_{0}+ 69 \cdot d= 1,000 + 69 \cdot (-3)= 1,000 - 207 = 793$ .

Report an Error

Example Question #2 : Nth Term Of An Arithmetic Sequence

The first two terms of an arithmetic sequence are 4 and 9, in that order. Give the one-hundredth term of that sequence.

Possible Answers:

494

899

499

904

504

Correct answer:

499

Explanation:

The first term is $x_{0} = 4$ ; the common difference is

d = 9-4 = 5 .

The hundredth term is

$x_{99} = x_{0} + 99 d = 4 + 99 \cdot5 = 4 + 495 = 499$ .

Report an Error

Example Question #3 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

-128, -124.7,...

Which of the following terms is the first positive term in the sequence?

Possible Answers:

The thirty-seventh term

The sequence has no positive terms.

The thirty-ninth term

The fortieth term

The thirty-eighth term

Correct answer:

The fortieth term

Explanation:

The common difference of the sequence is

-124.7 - (-128) = 3.3 ,

so the th term of the sequence is

$a_{n} = -128 + 3.3 (n-1)$

To find out the minimum value for which $a_{n} > 0$ , set up this inequality:

-128 + 3.3 (n-1) > 0

-128 + 3.3 n-3.3 > 0

3.3 n-131.3 > 0

3.3 n>131.3

n > 39.8

The first positive term is the fortieth term.

Report an Error

Example Question #4 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

5.7, 8.1,...

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

Possible Answers:

The fortieth term

The forty-third term

The forty-first term

The forty-fourth term

The forty-second term

Correct answer:

The forty-first term

Explanation:

The common difference of the sequence is

8.1 - 5.7 = 2.4

so the th term of the sequence is

$a_{n} =5.7+2.4 (n-1)$

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

5.7+2.4 (n-1) > 100

5.7+2.4 n-2.4 > 100

2.4 n +3.3 > 100

2.4 n > 96.7

$n > 96.7 \div 2.4 \approx 40.3$

The forty-first term is the correct response.

Report an Error

Example Question #12 : Arithmetic Sequences

An arithmetic sequence begins as follows:

300, 297.3,...

Which of the following terms is the first negative term in the sequence?

Possible Answers:

The one hundred fourteenth term

The one hundred thirteenth term

The one hundred eleventh term

The one hundred twelfth term

The one hundred tenth term

Correct answer:

The one hundred thirteenth term

Explanation:

The common difference of the sequence is

297.3 - 300 = -2.7

so the th term of the sequence is

$a_{n} = 300 -2.7 (n-1)$

To find out the minimum value for which $a_{n} < 0$ , set up this inequality:

300 -2.7 (n-1) < 0

300 -2.7 n+2.7 < 0

302.7-2.7 n < 0

302.7 < 2.7 n

2.7 n > 302.7

$n > 302.7 \div 2.7 \approx 112.1$

The first negative term is the one hundred thirteenth term.

Report an Error

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

An arithmetic sequence begins as follows:

$155 \frac{5}{6}, 153 \frac{3}{4},...$

Which of the following terms is the first negative term in the sequence?

Possible Answers:

The seventy-fourth term

The seventy-sixth term

The seventy-seventh term

The seventy-fifth term

The seventy-eighth term

Correct answer:

The seventy-sixth term

Explanation:

The common difference of the sequence is

$153 \frac{3}{4}- 155 \frac{5}{6}= -2 \frac{1}{12}$

so the th term of the sequence is

$a_{n} = 155\frac{5}{6}-\left (2 \frac{1}{12} \right )(n-1)$

To find out the minimum value for which $a_{n} < 0$ , set up this inequality:

$155\frac{5}{6}-\left (2 \frac{1}{12} \right )(n-1) < 0$

$155\frac{5}{6}-\left (2 \frac{1}{12} \right ) n + 2\frac{1}{12} < 0$

$157\frac{11}{12}-\left (2 \frac{1}{12} \right ) n < 0$

$157\frac{11}{12} < \left (2 \frac{1}{12} \right ) n$

$\left (2 \frac{1}{12} \right ) n > 157\frac{11}{12}$

$n > 157\frac{11}{12} \div 2 \frac{1}{12} = 75 \frac{4}{5}$

The seventy-sixth term is the first negative term.

Report an Error

Example Question #5 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

$-78 \frac{2}{3}, -75 \frac{4}{5},...$

Which of the following terms is the first positive term in the sequence?

Possible Answers:

The twenty-seventh term

The thirtieth term

The twenty-eighth term

The twenty-ninth term

The sequence has no positive terms.

Correct answer:

The twenty-ninth term

Explanation:

The common difference of the sequence is

$-75 \frac{4}{5} - \left ( -78 \frac{2}{3} \right ) =2 \frac{13}{15}$ ,

so the th term of the sequence is

$a_{n} = - 78\frac{2}{3} + \left ( 2\frac{13}{15} \right ) (n-1)$

To find out the minimum value for which $a_{n} > 0$ , set up this inequality:

$- 78\frac{2}{3} + \left ( 2\frac{13}{15} \right ) (n-1) > 0$

$- 78\frac{2}{3} + \left ( 2\frac{13}{15} \right ) n - 2\frac{13}{15} > 0$

$\left ( 2\frac{13}{15} \right ) n - 81\frac{8}{15} > 0$

$\left ( 2\frac{13}{15} \right ) n > 81\frac{8}{15}$

$n > 81\frac{8}{15} \div 2\frac{13}{15} = 28 \frac{19}{43}$

The first positive term in the sequence is the twenty-ninth term.

Report an Error

View SSAT- Upper Level Tutors

Joseph
Certified Tutor

Bank Street College of Education , Master's/Graduate, Early Childhood and Childhood General Education.

View SSAT- Upper Level Tutors

Peter
Certified Tutor

Syracuse University, Bachelor in Arts, English. Global Learning Teaching, Certificate, Teaching English as a Second Language ...

View SSAT- Upper Level Tutors

Darron
Certified Tutor

Georgia State University, Bachelors, English Education . Liberty University, Masters, Education.

All SSAT Upper Level Math Resources

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

Popular Subjects

Computer Science Tutors in Washington DC, French Tutors in Dallas Fort Worth, English Tutors in Houston, ACT Tutors in Philadelphia, Calculus Tutors in Dallas Fort Worth, SSAT Tutors in Miami, Statistics Tutors in Denver, LSAT Tutors in Chicago, English Tutors in Philadelphia, ISEE Tutors in Miami

Popular Courses & Classes

GRE Courses & Classes in New York City, ACT Courses & Classes in Phoenix, ACT Courses & Classes in Denver, Spanish Courses & Classes in San Diego, GMAT Courses & Classes in Atlanta, LSAT Courses & Classes in Seattle, ACT Courses & Classes in Washington DC, LSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Miami, ACT Test Prep in Denver, SSAT Test Prep in Chicago, LSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Miami, LSAT Test Prep in Atlanta, GMAT Test Prep in Phoenix, ACT Test Prep in Phoenix, LSAT Test Prep in Seattle, ACT 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

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 #11 : Arithmetic Sequences

Example Question #12 : Other Arithmetic Sequences

Example Question #13 : Other Arithmetic Sequences

Example Question #11 : Arithmetic Sequences

Example Question #2 : Nth Term Of An Arithmetic Sequence

Example Question #3 : Nth Term Of An Arithmetic Sequence

Example Question #4 : Nth Term Of An Arithmetic Sequence

Example Question #12 : Arithmetic Sequences

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

Example Question #5 : Nth Term Of An Arithmetic Sequence

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: