Let a be the first term and r be the common ratio of the G.P. According to the given condition,
a5 = a r5–1 = a r4 = p ………..… (1)
a8 = a r8–1 = a r7 = q ………….. (2)
a11 = a r11–1 = a r10 = s ………. (3)
Dividing equation (2) by (1), we obtain
Dividing equation (3) by (2), we obtain
Equating the values of r3 obtained in (4) and (5), we obtain
Thus, the given result is proved.