In an arithmetic sequence having terms natural numbers, prove that if

1.	In an arithmetic sequence having terms natural numbers, prove that if one of the terms is a perfect square, it will have more that this as the perfect square term.
Answer» As we know when a definite number of common difference of an arithmetic sequence is added to a term we get another term of the same sequence. If n² is a perfect square term, add (2n + d) times d to n². n² + (2n + d) x d = (n + d)². This is nothing but a perfect square term.

In an arithmetic sequence having terms natural numbers, prove that if one of the terms is a perfect square, it will have more that this as the perfect square term.

Answer»

As we know when a definite number of common difference of an arithmetic sequence is added to a term we get another term of the same sequence.

If n² is a perfect square term, add (2n + d) times d to n². n² + (2n + d) x d = (n + d)².

This is nothing but a perfect square term.

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In an arithmetic sequence having terms natural numbers, prove that if one of the terms is a perfect square, it will have more that this as the perfect square term.

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