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by jnbimmer » Sat Dec 19, 2009 12:43 am
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 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
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by papgust » Sat Dec 19, 2009 2:01 am
You can just plugin values to test the options. But alternatively, remember 2 points about AP. If an AP is subtracted/added with a constant, then the resulting sequence is still an AP. If an AP is multiplied/divided by a constant, then the resulting sequence is still an AP.

Assume the sequence is 1,4,7,10,13
I. 2, 8, 14, 20, 26 [The difference is 6. It is an AP]
II. -2, 1, 4, 7, 10 [The difference is still 3. It is an AP]
II. 1, 16, 49, 100, 169 [The difference is not constant. It is NOT an AP]
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by jnbimmer » Sat Dec 19, 2009 10:12 am
Thank you.
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