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, b, c, d are in G.P. and 1/c , 1/d,1/e are in A. P . Prove that a, c, e are in G.P.

If a,b,c are in A.P. b,c,d are in G.P. and 1/c,1/d,1/e are in A.P. prove that a,c,e are in G.P.

If a, b, c, are in A. P, and (b−a), (c−b), a are in G.P, then a : b : c is

If a, b, c are in A.P. and b-a,c-b and a are in G.P., then a:b:c is

Suppose that a,b,c,d are in G.P with common ratio r Prove that (b+c)(b+d)=(c+a)(c+d)

If a , a_(1) , a_(2) ,a_(3) , cdots a_(2n), b are in A.P. and a, g_(1) , g_(2) , g_(3) , cdots , g_(2n), b are in G.P. and h is the H.M of a and b then prove that (a_(1)+a_(2n))/(g_(1)g_(2n))+(a_(2)+a_(2n-1))/(g_(2)g_(2n-1))+cdots+ (a_(n)+a_(n+1))/(g_(n)g_(n+1))=(2n)/(h)

If a, b, c, d and p are different real numbers such that (a^2+b^2+c^2).p^2-2(ab+b c+cd) p +(b^2+c^2+d^2) le 0 , then show that a, b, c and d are in G.P .

If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+d x)/(c-d x)(x ne 0) , then show that a, b, c and d are in G.P.