The first four terms of a geometric sequence are \[a, \ b, \ 4a, \ a-6+b\] for some numbers \(a\) and \(b\) with \(a\neq 0\).
Determine all possibilities for the values of \(a\) and \(b\).
Note: A geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a non-zero constant, called the common ratio. For example, \(2\), \(6\), \(18\) is a geometric sequence with three terms and a common ratio of \(3\). You can explore geometric sequences further in our CEMC Courseware.