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.

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

The determinant Delta=|(a,b,ax+b),(b,c,bx+c),(ax+b,bx+c,c)| is equal to zero, if a)a,b,c are in A.P. b)a,b,c are in G.P. c)a,b,c are in H.P. d) ax^(2) + bx + c = 0

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

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)

Suppose that a,b,c,d are in G.P with common ratio r Prove that b+c=ar(1+r) and b+d=ar(1+r^2)