Let x , y and z be the respective sum of the first n terms, the next n terms and the next n terms of a geometric progression, then x , y , z are in

Step-by-step solution

Let A be the 1 st term and R be the common ratio of the given G.P. Sum of the first n terms of the G.P. is x = A ( 1 - R n ) 1 - R . The next n terms form a G.P. series of n terms with the first term as the n + 1 t h term of the given G.P. is given by t n + 1 = A R n . Sum of the next n terms of the G.P. is y ⇒ y = A R n ( 1 - R n ) 1 - R and z = A R 2 n 1 - R n 1 - R ⇒ y 2 = z x ∴ x , y , z are in G.P.