maths

Since r1,r2,r3,....rn is a geometric sequence
i.e.( rn/rn-1)=...=(r3/r2)=(r2/r1) ---( *)

Now , Consder
(r3)^3/(r2)^3=(r3/r2)^3
=(r2/r1)^3 By (*)
=(r2)^3/(r1)^3
In general (rn)^3/(rn-1)^3=...=(r3)^3/(r2)^3=(r2)^3/(r1)^3

i.e. r1^3,r2^3,r3^3,....rn^3 is also a geometric sequence.