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Can an arithmetic progression be formed where all the terms are squares? If yes, how many?

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maryinschool | Student, Grade 9 | eNotes Newbie

Posted November 26, 2010 at 10:28 PM via web

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Can an arithmetic progression be formed where all the terms are squares? If yes, how many?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted November 26, 2010 at 10:30 PM (Answer #1)

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In an arithmetic progression each term divided by the previous term has a common result.

The nth term of an arithmetic progression can be denoted by Tn = ar^ (n-1) where a is the first term and r is the common ratio.

If we need to create a series of squares which is also an arithmetic progression, it can be done as follows. Let the first term be a square and the common ratio also is a square. For example 4, 16, 64 … is an AP which has all terms as squares.

We can create an unlimited number of such series, we only need to ensure that for Tn = ar^ (n-1), a is a square and r is also a square.

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changchengliang | Elementary School Teacher | (Level 2) Adjunct Educator

Posted November 26, 2010 at 11:15 PM (Answer #2)

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Hi.

This answer may be thrown out very quickly.  Because I do not have 90 words to keep this entry here.

Take a look at this quick:

http://www.mathpages.com/home/kmath291.htm

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