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# p, r, s, t, u An arithmetic sequence is a sequence in which

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Joined: 04 May 2006
Posts: 1606
Schools: CBS, Kellogg
p, r, s, t, u An arithmetic sequence is a sequence in which  [#permalink]

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26 Feb 2008, 19:50
1
247. 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 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

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Joined: 22 Feb 2008
Posts: 5

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27 Feb 2008, 00:47

my answer is only I, II

In the case of arithmetic sequence,
you can presume "p = a + (n-1)*d ";

2p= 2*(a+(n-1)*d) = 2a + (n-1)*d
so, 2p is just the arithmetic sequence.

p-3 = (a+(n-1)*d)-3 = (a-3)+(n-1)*d
so, p-3 is also the arithmetic sequence.

p^2 = (a+(n-1)*d)^2 = a^2 + (n-1)^2*d^2
this is not the arithmetic sequence any more.
Director
Joined: 18 Feb 2008
Posts: 723

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27 Feb 2008, 13:36
1
I & II

just pick a number, much easier than doing the p -r ^ t x 2

1 4 7 10 13

I. 2 8 14 20 26 yes
II. -2 1 4 7 10 yes
III. 1 16 49 100 169 no

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Re: p, r, s, t, u An arithmetic sequence is a sequence in which  [#permalink]

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06 Apr 2019, 23:45
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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).

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Re: p, r, s, t, u An arithmetic sequence is a sequence in which   [#permalink] 06 Apr 2019, 23:45
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