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 $\tfrac{30 \cdot 392}{2} = \boxed{\textbf{(A)}\ 5880}$.

See Also

1973 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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