Let and are positive real numbers. If are in arithmetic progression are in G.P. and are in H.P. show that...

Since are in A.P. are in G.P. are in H.P. (From (1) and (2)) We also know , are in H.P. We get and similarly for Substituting...

Let a and b are positive real numbers. If a, A_1, A_2, b are in arithmetic progression a, G_1, G_2, b are in G.P. and a, H_1, H_2, b are in H.P. show that \frac{G_1 G_2}{H_1 H_2}=\frac{A_1+A_2}{H_1+H_2}=\frac{(2 a+b)(a+2 b)}{9 a b}: Sequence & Series (Mathematics)

Let

a

and

b

are positive real numbers. If

a, A_1, A_2, b

are in arithmetic progression

a, G_1, G_2, b

are in G.P. and

a, H_1, H_2, b

are in H.P. show that

\frac{G_1 G_2}{H_1 H_2}=\frac{A_1+A_2}{H_1+H_2}=\frac{(2 a+b)(a+2 b)}{9 a b}