12. An arithmetic progression has first term \(a\) and common difference \(d\), where \(a\) and \(d\) are non-zero. The first, third and fourth terms of the arithmetic progression are consecutive terms of a geometric progression with common ratio \(r\).
- Show that \(r = \frac { a + 2 d } { a }\).
- Find \(d\) in terms of \(a\).
- Find the common ratio of the geometric progression.
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