If the 5th term of an arithmetic sequence is 11 and the 16th term is -77, what is the 20th term?

Recommended textbooks for you

College Algebra

Publisher:Cengage Learning

Glencoe Algebra 1, Student Edition, 9780079039897...

Intermediate Algebra

Publisher:OpenStax College

Algebra & Trigonometry with Analytic Geometry

College Algebra (MindTap Course List)

Author:R. David Gustafson, Jeff Hughes

Publisher:Cengage Learning

College Algebra

ISBN:9781337282291

Author:Ron Larson

Publisher:Cengage Learning

Glencoe Algebra 1, Student Edition, 9780079039897...

ISBN:9780079039897

Author:Carter

Publisher:McGraw Hill

Intermediate Algebra

ISBN:9780998625720

Author:Lynn Marecek

Publisher:OpenStax College

Algebra & Trigonometry with Analytic Geometry

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

College Algebra (MindTap Course List)

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:Cengage Learning

The first term of an arithmetic sequence is

; the fifth term is

. What is the second term?

Possible Answers:

Correct answer:

Explanation:

To find the common difference

, use the formula

For us,

and

Now we can solve for

Add the common difference to the first term to get the second term.

The sum of the first three terms of an arithmetic sequence is 111 and the fourth term is 49. What is the first term?

Possible Answers:

It cannot be determined from the information given.

Correct answer:

Explanation:

Let

be the common difference, and let

be the second term. The first three terms are, in order,

The sum of the first three terms is

Now we know that the second term is 37. The fourth term is the second term plus twice the common difference:

. Since the second and fourth terms are 37 and 49, respectively, we can solve for the common difference.

The common difference is 6. The first term is

An arithmetic sequence begins with

. If

is the first term in the sequence, find the 31st term.

Possible Answers:

Correct answer:

Explanation:

For arithmetic sequences, we use the formula , where

is the term we are trying to find,

is the first term, and

is the difference between consecutive terms. In this case,

and

. So, we can write the formula as

, and

The fourth and tenth terms of an arithmetic sequence are 372 and 888, respectively. What is the first term?

Possible Answers:

Correct answer:

Explanation:

Let

be the common difference of the sequence. Then

, or, equivalently,

, or equivalently,

The ninth and tenth terms of an arithmetic sequence are, respectively, 87 and 99. What is its first term?

Possible Answers:

Correct answer:

Explanation:

The common difference of the sequence is the difference of the tenth and ninth terms:

The ninth term of an arithmetic sequence with first term

and common difference

, so we set this equal to 87, set

, and solve:

The eighth and tenth terms of an arithmetic sequence are, respectively, 87 and 99. What is its first term?

Possible Answers:

Correct answer:

Explanation:

The eighth and tenth terms of the sequence are

and

, where

is the first term and

is the common difference. We can find the common difference by subtracting the tenth and eighth terms and solving for

Now set eighth term

equal to 87, set

, and solve:

Find the 100th term in the following arithmetic sequence

Possible Answers:

Correct answer:

Explanation:

Before we can figure out the 100th term, we need to find a rule for this arithmetic sequence. Remember, the general rule for this sequence is

where

represents the first number in the sequence,

is the common difference between consecutive numbers, and

is the

-th number in the sequence.

In our problem,

. Also, each time we move up from one number to another, the number increases by 7. Therefore,

. So the rule for this sequence is written as

Now that we found our rule, we can go on and figure out what the 100th term is equal to. For the 100th term,

. Thus

To find any term of an arithmetic sequence:

Where

is the first term,

is the number of the term to find, and

is the common difference in the sequence.

Find the 18th term of the following arithmetic sequence.

Possible Answers:

Correct answer:

Explanation:

Start by finding the common difference,

, in this sequence, which you can get by subtracting the first term from the second.

Then, using the formula given before the question:

To find any term of an arithmetic sequence:

Where

is the first term,

is the number of the term to find, and

is the common difference in the sequence.

Find the 26th term of the following arithmetic sequence.

Possible Answers:

Correct answer:

Explanation:

Start by finding the common difference in terms by subtracting the first term from the second.

Then, fill in the rest of the equation given before the question.

Given the the sequence below, what is the 11th term of the sequence?

1, 5, 9, 13, . . .

Possible Answers:

Explanation:

The 11th term means there are 10 gaps in between the first term and the 11th term. Each gap has a difference of +4, so the 11th term would be given by 10 * 4 + 1 = 41.

The first term is 1.

Each term after increases by +4.

The nth term will be equal to 1 + (n – 1)(4).

The 11th term will be 1 + (11 – 1)(4)

1 + (10)(4) = 1 + (40) = 41

Sanford
Certified Tutor

University of Florida, Bachelor of Science, Mathematics. Air Force Institute of Technology-Graduate School of Engineering Ma...

Elan
Certified Tutor

University of Cambridge, Bachelor in Arts, Engineering Physics. University of Illinois at Urbana-Champaign, Doctor of Philoso...

Jacqueline
Certified Tutor

University of North Carolina at Asheville, Bachelor in Arts, Mathematics. Western Carolina University, Doctor of Education, E...

If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

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: