1973 AHSME Problems/Problem 7

Problem

The sum of all integers between 50 and 350 which end in 1 is

$\textbf{(A)}\ 5880\qquad\textbf{(B)}\ 5539\qquad\textbf{(C)}\ 5208\qquad\textbf{(D)}\ 4877\qquad\textbf{(E)}\ 4566$

Solution

The numbers that we are adding are $51,61,71 \cdots 341$ . The numbers are part of an arithmetic series with first term $51$ , last term $341$ , common difference $10$ , and $30$ terms. Using the arithmetic series formula, the sum of the terms is $\tfrac{30 \cdot 392}{2} = \boxed{\textbf{(A)}\ 5880}$ .

1973 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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1973 AHSME Problems/Problem 7

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