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An arithmetic sequence is a sequence in which each term [#permalink]
25 Jan 2008, 12:53

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Difficulty:

25% (medium)

Question Stats:

68% (02:02) correct
32% (00:58) wrong based on 314 sessions

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: arithmetic sequence [#permalink]
25 Jan 2008, 13:00

blog wrote:

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]
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 _________________

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

Re: An arithmetic sequence is a sequence in which each term [#permalink]
10 May 2014, 04:12

Expert's post

russ9 wrote:

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)

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]
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 _________________

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