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Arithmetic mean of first n positive integers

Source: 1959 AHSME Problem 18

August 13, 2013

arithmetic sequenceAMCarithmetic meanarithmetic seriesalgebraAMC 12

Problem Statement

The arithmetic mean (average) of the first

n

positive integers is:

<span class='latex-bold'>(A)</span>\ \frac{n}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac{n^2}{2}\qquad<span class='latex-bold'>(C)</span>\ n\qquad<span class='latex-bold'>(D)</span>\ \frac{n-1}{2}\qquad<span class='latex-bold'>(E)</span>\ \frac{n+1}{2}