# Just arithmetic

Algebra Level 3

An arithmetic progression consisting of $$n$$ terms which are alternatively odd and even has its first term $$a$$ an odd positive integer and common difference $$d$$ also a positive integer.

When the sum of the first, third, fifth, seventh, ... terms are subtracted from the sum of the second, fourth, sixth, eight, ... terms, the result obtained is 501. Find $$n × d$$.

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