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If \( 1,2,3 \ldots \) are first terms; \( 1,3,5 \ldots \) are common differences and \( S_{1}, S_{2}, S_{3} \ldots \). are sums of \( n \) terms of given \( p \) AP's; then \( \mathrm{S}_{1}+\mathrm{S}_{2}+\mathrm{S}_{3}+\ldots+\mathrm{S}_{\mathrm{p}} \) is equal to
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(A) \( \frac{n p(n p+1)}{2} \)
(B) \( \frac{n(n p+1)}{2} \)
(C) \( \frac{n p(p+1)}{2} \)
(D) \( \frac{n p(n p-1)}{2} \)
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