1957 AHSME Problems/Problem 30

Problem

The sum of the squares of the first n positive integers is given by the expression $\frac{n(n + c)(2n + k)}{6}$ , if $c$ and $k$ are, respectively:

$\textbf{(A)}\ {1}\text{ and }{2} \qquad \textbf{(B)}\ {3}\text{ and }{5}\qquad \textbf{(C)}\ {2}\text{ and }{2}\qquad\textbf{(D)}\ {1}\text{ and }{1}\qquad\textbf{(E)}\ {2}\text{ and }{1}$

Solution

When $n=1$ , the value of the given expression must be $1^2=1$ . Plugging in the values given by the answer choices, we see that the only option that returns $1$ when $n=1$ is $\boxed{\textbf{(D) }1 \text{ and } 1}$ .

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 29	Followed by Problem 31
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1957 AHSME Problems/Problem 30

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