1959 AMC 12 Problem 18

Attempt Problem 18 of the 1959 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1959 AMC 12 solutions, or check the answer key.

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18.

The arithmetic mean (average) of the first

n

positive integers is:

\dfrac n2

\dfrac{n^2}{2}

n

\dfrac{n-1}{2}

\dfrac{n+1}{2}

Use the sum

1+2+\cdots+n

Divide the sum by the number

n

of terms

The sum of the first

n

positive integers is

\frac{n(n+1)}{2}.

Dividing by

n

gives the mean

\frac{n+1}{2}.

Therefore, the correct answer is E.

Problem 18 in other years