The first three terms of an arithmetic progression are \(2 x , x + 4\) and \(2 x - 7\) respectively. Find the value of \(x\).
The first three terms of another sequence are also \(2 x , x + 4\) and \(2 x - 7\) respectively.
(a) Verify that when \(x = 8\) the terms form a geometric progression and find the sum to infinity in this case.
(b) Find the other possible value of \(x\) that also gives a geometric progression.