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

Expert Answers
justaguide eNotes educator| Certified Educator

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.

changchengliang eNotes educator| Certified Educator


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