4 The positive integers \(x , y\) and \(z\) are the first, second and third terms, respectively, of an arithmetic progression with common difference - 4 .
Also, \(x , \frac { 15 } { y }\) and \(z\) are the first, second and third terms, respectively, of a geometric progression.
- Show that \(y\) satisfies the equation \(y ^ { 4 } - 16 y ^ { 2 } - 225 = 0\).
- Hence determine the sum to infinity of the geometric progression.