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2013 AMC 12A Question 7

AMC12 · 2013 AMC 12A

Question 7

The sequence $S_1,$ $S_2,$ $S_3,$ $\ldots,$ $S_{10}$ 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 $S_4?$
  1. $4$
  2. $6$
  3. $10$
  4. $12$
  5. $16$