The sum of an arithmetic sequence with 600 terms is 120000; Last term=393 Find the common difference

Derivation of the sum formula for an arithmetic progression depends on the the closed sum formula for the first n-1 positive integers. The formula is (First Term + Second Term)n/2 where n is the number of terms in the arithmetic sequence. The primality of 599 ensures that only the first and last terms are natural numbers!
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A. E. Ingham, H. Davenport, T. Estermann, H. Halberstam, J. H. H. Chalk, and P. T. Bateman