Monday, April 7, 2014

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

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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