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An arithmetic sequence is a sequence in which each term [#permalink]
 25 Jan 2008, 13:53
Question Stats:
66% (01:34) correct
33% (00:45) wrong based on 59 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
Last edited by Bunuel on 01 Nov 2012, 08:44, edited 1 time in total.
Renamed the topic, edited the question and moved to PS forum.
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Re: arithmetic sequence [#permalink]
25 Jan 2008, 14:00
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
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Re: arithmetic sequence [#permalink]
25 Jan 2008, 14:09
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]
21 Jul 2010, 22:42
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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]
09 Aug 2010, 08:49
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]
01 Nov 2012, 01:52
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]
27 Jan 2013, 04:31
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]
27 Jan 2013, 04:31
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