Question

If a, b, c are in A.P. and geometric means of ac and ab, ab and bc, ca nad cb are d, e, f respectively then d² , e² , f² are in _____ 

(A) A. P. 

(B) G. P. 

(C) H. P. 

(D) A. G. P.

Answer 1

The correct option is (A) A. P.

Explanation:

Since d is G.M. between ac and ab 

d² = ac . ab = a²bc 

similarly e² = ab² c and f² = abc² 

Now a, b, c in A.P 

a²bc, ab² c, abc² in A.P.

d² , e² f² are in A.P.