FIITJEE A.P Problem

Algebra Level 2

Given $$p$$ arithmetic progressions, each of which consisting of $$n$$ terms, if their first terms are $$1,2,3,\ldots,p-1,p$$ and common differences are $$1,3,5,7,\ldots,2p-3,2p-1,$$ respectively, what is the sum of all the terms of all the arithmetic progressions?

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