Progressions are not as easy as you think

Algebra Level 4

If \(x\), \(y\) and \(z\) are in geometric progression and \(x\), \(2y\) and \(3z\) are in arithmetic progression, find the common ratio of the geometric progression.

Note: \(x\), \(y\) and \(z\) are distinct, non zero integers.

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