If a,b,c,d are in G.P., show that `a^2 - b^2,b^2-c^2,c^2-d^2` are in G.P.

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

If a,b,c, d are in G.P., show that : a^(2)+b^(2), b^(2)+ c^(2) and c^(2)+d^(2) are also in G.P.

If a, b, c and d are in G.P. show that (a^2+ b^2+ c^2) (b^2 + c^2 + d^2)= ( ab + bc + cd)^2 .

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (c^(n) + d^(n)) are in G.P.

If a, b, c are in A.P., prove that : (b+c)^2-a^2, (c+a)^2-b^2, (a+b)^2-c^2 are also in A.P.

If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2) .

If a,b,c are in A.P. and a^2,b^2,c^2 are in H.P. then which of the following could and true (A) -a/2, b, c are in G.P. (B) a=b=c (C) a^3,b^3,c^3 are in G.P. (D) none of these

If a^2 (b+c),b^2(c+a) , c^2(a+b) are in A.P., show that : either a, b, c are in A.P. or ab + bc + ca =0.

If a, b,c are in G.P, then log a, log b, log c are: