Show that the products of the corresponding terms of the sequences a, `a r ,a r^2,dotdotdot,a r^(n-1)`and `A ,A R ,A R^2,dotdotdot,A R^(n-1),`form a G.P, and find the common ratio.

Show that the products of the corresponding terms of the sequences a ,\ a r ,\ a r^2,ddot,\ a r^(n-1)\ a n d\ A ,\ A R ,\ A R^2,\ ,\ A R^(n-1)\ form a G.P. and find the common ratio.

Show that the products of the corresponding terms of the sequences a,ar,ar^2,…ar^(n-1) and A,AR,AR^2,….AR^(n-1) form n G.P. and find the C.R.

Show that the ratio of the sum of first n terms of a G.P. and the sum of (n+1)th term to (2n)th term is (1)/(r^(n)) .

Show that the ratio of the sum of first n terms of a G.P. and the sum of (n+1)th term to (2n)th term is (1)/(r^(n)) .

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n+1) to (2n) terms is (1)/(r^(n))

Prove that the sum of n terms of GP with first term a and common ratio r is given by S_(n)=a(r^(n)-1)/(r-1)

if S is the sum,P the product and R the sum of reciprocals of n terms in G.P. prove that P^(2)R^(n)=S^(n)