Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

An arithmetic sequence is a sequence in which each term [#permalink]

Show Tags

25 Jan 2008, 12:53

2

This post received KUDOS

13

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

72% (02:01) correct
28% (01:05) wrong based on 1049 sessions

HideShow timer Statistics

p, r, s, t, u

An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

I. 2p, 2r, 2s, 2t, 2u II. p-3, r-3, s-3, t-3, u-3 III. p^2, r^2, s^2, t^2, u^2

(A) I only (B) II only (C) III only (D) I and II (E) II and III

An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

1.) 2p, 2r, 2s, 2t, 2u 2.) p-3, r-3, s-3, t-3, u-3 3.) p square, r square, s square, t square, u square.

(A)1 only (B)2 only (C)3 only (D)1 and 2 (E)2 and 3

D.

Picking numbers is great for this problem:

For example: if the arithmetic sequence is 5,7,9,11,.... 1) 10,14,18,22.... is still an arithmetic sequence 2) 2,4,6,8....... is still an arithmetic sequence 3) is not an arithmetic sequence

The first sentence defines an arithmetic sequence. For example, {5, 10, 15, 20, 25} is an arithmetic sequence.

When you have a roman numeral question, start with either a) the roman numeral that is easiest to evaluate or else b) the roman numeral that appears most frequently among the answer choices.

Let's start with II because it shows up the most (three times). Using our example above ({5, 10, 15...}), we can see that {2, 7, 12...} will also be an arithmetic sequence....eliminate A and C (because they don't contain II).

Let's look at I because it is easier than III. If {5, 10, 15...} is an arithmetic sequence, then clearly {10, 20, 30...} is also an arithmetic sequence....eliminate B and E (because they don't contain I).

The correct answer must be D!

(And there is no need to evaluate III--which is fortunate since I wasn't sure what you meant by "p2, r2" although I guess you mean squares).

Re: An arithmetic sequence is a sequence in which each term [#permalink]

Show Tags

27 Jan 2013, 03:31

1

This post received KUDOS

I followed a mixed approach. Started by picking numbers and realized soon that option 3 would not give me the results
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: An arithmetic sequence is a sequence in which each term [#permalink]

Show Tags

23 Mar 2014, 17:05

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: An arithmetic sequence is a sequence in which each term [#permalink]

Show Tags

09 May 2014, 14:26

Hi,

Can someone please clarify a nagging issue:

For a sequence to be an arithmetic sequence, does the different between the units have to be constant? To elaborate, are all three examples below considered arithmetic sequences?

-[2,4,6,8] = difference of 2 -[3,9,81...] = all the units are squared but the differences are not constant -[2, 5, 9, 14]= the difference is 2+1 so (5= 2 + 3), (9=3+4), (14 = 9 + 5)

For a sequence to be an arithmetic sequence, does the different between the units have to be constant? To elaborate, are all three examples below considered arithmetic sequences?

-[2,4,6,8] = difference of 2 -[3,9,81...] = all the units are squared but the differences are not constant -[2, 5, 9, 14]= the difference is 2+1 so (5= 2 + 3), (9=3+4), (14 = 9 + 5)

Arithmetic Progression is a special type of sequence in which the difference between successive terms is constant.

{2, 4, 6, 8} is an arithmetic progression (the difference = 2). {3, 9, 81} is neither arithmetic not geometric progression. {2, 5, 9, 14} is neither arithmetic not geometric progression.

Re: An arithmetic sequence is a sequence in which each term [#permalink]

Show Tags

10 May 2014, 04:59

blog wrote:

p, r, s, t, u

An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

I. 2p, 2r, 2s, 2t, 2u II. p-3, r-3, s-3, t-3, u-3 III. p^2, r^2, s^2, t^2, u^2

(A) I only (B) II only (C) III only (D) I and II (E) II and III

Best thing should be plug in:

p = 1, q = 2, r = 3, s = 4, t = 5

I. 2, 4, 6, 8, 10 (Arithmetic Progression) II. -2, -1, 0, 1, 2 (Arithmetic Progression) III. 1, 4, 9, 16, 25 (Not AP)

Hence I and II
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Arithmetic Sequence question= Need Help! [#permalink]

Show Tags

09 Mar 2015, 14:58

p,r,s,t,u

An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. if the list of letters shown above is an arithmetic sequence, which of the following must also also be an arithmetic sequence?

I. 2p,2r,2s,2t,2u II. p-3,r-3,s-3,t-3,u-3 III. p^2,r^2,s^2,t^2,u^2

(A) I only (B) II only (C) III only (D) I and II (E) II and III

An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. if the list of letters shown above is an arithmetic sequence, which of the following must also also be an arithmetic sequence?

I. 2p,2r,2s,2t,2u II. p-3,r-3,s-3,t-3,u-3 III. p^2,r^2,s^2,t^2,u^2

(A) I only (B) II only (C) III only (D) I and II (E) II and III

An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. if the list of letters shown above is an arithmetic sequence, which of the following must also also be an arithmetic sequence?

I. 2p,2r,2s,2t,2u II. p-3,r-3,s-3,t-3,u-3 III. p^2,r^2,s^2,t^2,u^2

(A) I only (B) II only (C) III only (D) I and II (E) II and III

as we know an arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant... this means the difference between each consecutive number is constant.... lets look at the three choices... I. 2p,2r,2s,2t,2u.... since the difference is constant,say x and each number has been multiplied by a constant 2, the difference too will remain 2x... so it will be an arithmetic sequence...

II. p-3,r-3,s-3,t-3,u-3 since the difference is constant,say again x and each number has been subtracted by a constant 3 , the difference too will remain x-3... so it will be an arithmetic sequence...

III. p^2,r^2,s^2,t^2,u^2 since the difference is constant in initial sequence ,say x and now, each number has been multiplied by itself. Basically it means that each term is being multiplied by a different number, which is equal to itself... the difference now will change for each two consecutive number ... so it will not be an arithmetic sequence...

Re: An arithmetic sequence is a sequence in which each term [#permalink]

Show Tags

16 Aug 2015, 16:09

The list of letters is bugging me, specifically because there is a gap between p and r (q). Is this relevant or just a distraction in the question? A simple explanation would be very helpful! Thank you!

The list of letters is bugging me, specifically because there is a gap between p and r (q). Is this relevant or just a distraction in the question? A simple explanation would be very helpful! Thank you!

Valid question, but it is an official question. It is what it is and you can not question the language or the OA for the question.

I dont believe knowing the alphabets in a particular sequence is relevant for this question. GMAT can even give us strange symbols to stand for these variables. You just have to understand what is an arithmetic progression and after that it is all a matter solving the question with whatever variables are given to you.

If GMAT wants to give you a,z,y,b,c and say that they are in arithmetic progression (ie difference between 2 consecutive terms is constant and is the same value), then you have to stick to this pattern of variables.

Re: An arithmetic sequence is a sequence in which each term [#permalink]

Show Tags

21 Nov 2015, 07:00

Please tag Sequence as this is Arithmetic Series question. Thank you.

blog wrote:

p, r, s, t, u

An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

I. 2p, 2r, 2s, 2t, 2u II. p-3, r-3, s-3, t-3, u-3 III. p^2, r^2, s^2, t^2, u^2

(A) I only (B) II only (C) III only (D) I and II (E) II and III

Re: An arithmetic sequence is a sequence in which each term [#permalink]

Show Tags

15 Jun 2016, 05:03

blog wrote:

p, r, s, t, u

An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

I. 2p, 2r, 2s, 2t, 2u II. p-3, r-3, s-3, t-3, u-3 III. p^2, r^2, s^2, t^2, u^2

(A) I only (B) II only (C) III only (D) I and II (E) II and III

The defining factor of an arithmetic sequence is that there is a constant difference d between each pair of successive terms.

We are given an arithmetic sequence p, r, s, t, u. We need to determine which of the following MUST also be an arithmetic sequence. An easy way to determine this will be to choose convenient numbers for our initial sequence. Let's let the sequence look like this:

p, r, s, t, u = 2, 4, 6, 8, 10. Notice that the constant difference between each pair of successive terms is d = 2, and thus we are assured that it is an arithmetic sequence.

We can now use these numbers in the sequences presented in the three statements.

Statement I: 2p, 2r, 2s, 2t, 2u → (2 x 2), (2 x 4), (2 x 6), (2 x 8), (2 x 10) → 4, 8, 12, 16, 20

Notice that the above number set follows the definition of an arithmetic sequence, with a constant difference of d = 4. Thus, Statement I MUST be true.

We can eliminate answer choices B, C, and E.

Statement II. (p – 3), (r – 3), (s – 3), (t – 3), (u –3) →

(2 – 3), (4 – 3), (6 – 3), (8 – 3), (10 – 3) →

-1, 1, 3, 5, 7

Notice that the above number set follows the definition of an arithmetic sequence, with a constant difference of d = 2. Thus, Statement II MUST be true.

We can eliminate answer choice A. Even though we know that D is the correct answer choice, let’s check statement III anyway.

Statement III. p^2, r^2, s^2, t^2, u^2 →

2^2, 4^2, 6^2, 8^2, 10^2 →

4, 16, 36, 64, 100

Notice that the above number set DOES NOT follow the definition of an arithmetic sequence because there is not a constant difference between each pair of successive terms in the set. Thus, Statement III is NOT true.

Answer D

Note: Note that in the answer choices presented, the option “I, II, and III” is not given. Thus, once we determined that I and II were true we could have immediately chosen D as our answer.
_________________

Jeffrey Miller Scott Woodbury-Stewart Founder and CEO

gmatclubot

Re: An arithmetic sequence is a sequence in which each term
[#permalink]
15 Jun 2016, 05:03

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...