If a,b,c,d are in G.P than show that ab,ca,bc,bd` are also in G.P.

If a,b,c are in G.P., show that 1/(a+b),1/(2b),1/(b+c) are in A.P.

If a,b,c are in G.P then show that a(b^2-c^2)=c(a^2-b^2)

If a,b,c are in G.P then show that a(b^2+c^2)=c(a^2+b^2)

If a, b, c are in A.P. and a,b, d are in G.P., prove that a, a-b, d-c are in G.P.

If x,y,z are in G.P then show that log x,log y,log z are in A.P. (x>0,y>0,z>0) .

If a,b,c are in G.P then show that (a+2b+2c)(a-2b+2c)=a^2+4c^2

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P. show that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

If a,b,c,d are in G.P show that each of the following three term are also in G.P a^2+b^2+c^2,ab+bc+cd,b^2+c^2+d^2 .

If a,b,c,d are in G.P show that each of the following three term are also in G.P a+b,b+c,c+d .

If a, b, c, d are in G.P., show that each of the following three term are also in G.P. a+b,b+c,c+d .