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

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p, r, s, t, u An arithmetic sequence is a sequence in which [#permalink] New post 26 Feb 2008, 18:50
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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Re: 247. sequence [#permalink] New post 26 Feb 2008, 23:47
:roll:

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.
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Re: 247. sequence [#permalink] New post 27 Feb 2008, 12:36
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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
Re: 247. sequence   [#permalink] 27 Feb 2008, 12:36
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