# Problem #1757

 1757 The sequence $S_1, S_2, S_3, \cdots, S_{10}$ has the property that every term beginning with the third is the sum of the previous two. That is, $$S_n = S_{n-2} + S_{n-1} \text{ for } n \ge 3.$$ Suppose that $S_9 = 110$ and $S_7 = 42$. What is $S_4$? $\textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 16\qquad$ This problem is copyrighted by the American Mathematics Competitions.
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