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kaliprasad
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find parametetric representation of 3 perfect squares which are successive terms in AP ($x^2$,$y^2$,$z^2$) such that $x^2,y^2,z^2$ are successive terms of AP. find x,y,z
kaliprasad said:find parametetric representation of 3 perfect squares which are successive terms in AP ($x^2$,$y^2$,$z^2$) such that $x^2,y^2,z^2$ are successive terms of AP. find x,y,z
An AP, or arithmetic progression, is a sequence of numbers where the difference between consecutive terms is constant.
This means that each term in the sequence is a perfect square number, such as 1, 4, 9, 16, etc.
You can determine this by finding the common difference between the consecutive terms and checking if it is a perfect square. If it is, then the 3 consecutive terms are perfect squares.
Yes, an AP can have any number of consecutive terms that are perfect squares, as long as the common difference between them is a perfect square.
One example is the sequence 9, 16, 25. Another example is 1, 4, 9. Both of these sequences have a common difference of 7, which is a perfect square.