# Arithmetic and Geometric Sequences Together

Level pending

Suppose $$x,y,z$$ is a geometric sequence with a common ratio of $$r$$ where $$r \neq 1$$. If $$3x, 26y, 17z$$ is an arithmetic sequence, then the sum of all possible values of $$r$$ can be expressed as $$\dfrac{m}{n}$$. Find $$m+2n$$.

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