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Sum of the first 4n positive integers

Source: 1970 AHSME Problem 22

March 24, 2014
AMC

Problem Statement

If the sum of the first 3n3n positive integers is 150150 more than the sum of the first nn positive integers, then the sum of the first 4n4n positive integers is
<spanclass=latexbold>(A)</span>300<spanclass=latexbold>(B)</span>350<spanclass=latexbold>(C)</span>400<spanclass=latexbold>(D)</span>450<spanclass=latexbold>(E)</span>600<span class='latex-bold'>(A) </span>300\qquad<span class='latex-bold'>(B) </span>350\qquad<span class='latex-bold'>(C) </span>400\qquad<span class='latex-bold'>(D) </span>450\qquad <span class='latex-bold'>(E) </span>600