Let the A.P. be \(a, a+d, a+2d, \ldots\) The 2nd term is \(a+d\), 5th term is \(a+4d\), and 9th term is \(a+8d\). For these to be in G.P.: \((a+4d)^2 = (a+d)(a+8d)\). Expanding: \(a^2 + 8ad + 16d^2 = a^2 + 9ad + 8d^2\), which simplifies to \(8d^2 = ad\). Since the A.P. is non-constant, \(d \neq 0\), so \(a = 8d\). The three terms become \(9d, 12d, 16d\). Common ratio = \(\frac{12d}{9d} = \frac{4}{3}\).