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An arithmetic sequence is a sequence in which each term

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

Last edited by Bunuel on 01 Nov 2012, 07:44, edited 1 time in total.
Renamed the topic, edited the question and moved to PS forum.
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Re: arithmetic sequence [#permalink] New post 25 Jan 2008, 13:00
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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
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Re: arithmetic sequence [#permalink] New post 25 Jan 2008, 13:09
D is the answer

a(n) = a(n-1) + d

1) b(n) = 2*a(n) = 2*a(n-1)+2*d = b(n-1)+2*d -> arithmetic (d_new = 2*d)
2) b(n) = a(n) - c = a(n-1)+d-c = a(n-1)-c+d = b(n-1) + d -> arithmetic
3) b(n) = a(n)^2 = a(n-1)^2 + 2*a(n-1)*d + d^2 = b(n-1) + 2*a(n-1)*d + d^2 <> b(n-1) + const -> not arithmetic
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Re: OG12 - PS - Q228 [#permalink] New post 21 Jul 2010, 21:42
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Hi masland,

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).
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Re: OG12 - PS - Q228 [#permalink] New post 09 Aug 2010, 07:49
From the definition you can clearly see that II is an arithmetic sequence. III is clearly not.

Option I is a trap! If you expand it to \(p+p, r+r, s+s, t+t, u+u\) it appears it doesn't increase by a constant.

If you rewrite the original sequence with an increase of \(n\) you get, \(p, p + n, p + 2n, p+3n, p+4n\).

Now multiply it by 2, and get \(2p, 2p + 2n, 2p + 4n, 2p + 6n, 2p + 8n\). Now you can see that I increases by \(2n\)!
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Re: An arithmetic sequence is a sequence in which each term [#permalink] New post 01 Nov 2012, 00:52
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1) multiples all the terms by 2
2) subtracts all the terms by 3..

They gotto be in arithmetic sequence

whereas 3 squares .. anythign when squared will increase the value by a huge value. . and arithmetic sequence may not be maintained
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Re: An arithmetic sequence is a sequence in which each term [#permalink] New post 27 Jan 2013, 03:31
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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] New post 23 Mar 2014, 17:05
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Re: An arithmetic sequence is a sequence in which each term [#permalink] New post 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)
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Re: An arithmetic sequence is a sequence in which each term [#permalink] New post 10 May 2014, 04:12
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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.

Theory on sequences problems: sequences-progressions-101891.html

All DS sequences problems to practice: search.php?search_id=tag&tag_id=111
All PS sequences problems to practice: search.php?search_id=tag&tag_id=112

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Re: An arithmetic sequence is a sequence in which each term [#permalink] New post 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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Arithmetic Sequence question= Need Help! [#permalink] New post 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
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Re: An arithmetic sequence is a sequence in which each term [#permalink] New post 09 Mar 2015, 15:00
Expert's post
mawus wrote:
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


Merging topics.

Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1,2, 3, 7, 8, and 10. Thank you.


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Re: An arithmetic sequence is a sequence in which each term [#permalink] New post 10 Mar 2015, 00:35
mawus wrote:
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


hi mawus,

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...

only l and ll.. ans D....
Re: An arithmetic sequence is a sequence in which each term   [#permalink] 10 Mar 2015, 00:35
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