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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