Mock AIME 1 2006-2007 Problems/Problem 13

Problem

Let $a_{n}$ , $b_{n}$ , and $c_{n}$ be geometric sequences with different common ratios and let $a_{n}+b_{n}+c_{n}=d_{n}$ for all integers $n$ . If $d_{1}=1$ , $d_{2}=2$ , $d_{3}=3$ , $d_{4}=-7$ , $d_{5}=13$ , and $d_{6}=-16$ , find $d_{7}$ .

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Mock AIME 1 2006-2007

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Mock AIME 1 2006-2007 Problems/Problem 13

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