An algebra problem by Paola Ramírez

Algebra Level 3

The first four terms of an arithmetic sequence are \(a+b,a-b,ab\) and \(\frac{a}{b}\).

If the 5th term can be written as \(\dfrac mn\), where \(m\) and \(n\) are coprime positive integers, find the value of \(m+n\).


This problem is not original.
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