A hidden GP in an AP!

Algebra Level 2

The \(2nd\), \(6th\) and \(8th\) terms of an Arithmetic Progression form a Geometric Progression. The common ratio of the G.P can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime integers. What is the value of \(a+b\)?

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