Problems with AP and GP

It is typical to some terms of an arithmetic sequence happen to form some terms of a geometric sequence, though such would necessarily involve only a finite number of terms. To avoid confusion, we usually invoke two different symbols, say \(u_n\) and \(v_n\) to stand for the two different sequences.

The \(1^{\mathrm{st}}\), \(4^{\mathrm{th}}\) and \(8^{\mathrm{th}}\) terms of an arithmetic sequence, with common difference \(d, d \neq 0\) are the first three terms of a geometric sequence, with common ration \(r\). Given that the first term of both sequences is \(9\) find

1. the value of \(d\) ;
2. the value of \(r\) .