Question

If a,b,c are in G.P. and a¹/x = b¹/y = c¹/z ,prove that x,y,z are in A.P.
From A.P and G.P. from 11 class

Answer 1

I am in 10th class ...

Let a^(1/x) = b^(1/y) = c^(1/z) = k

= > a = k^x

= > b = k^y

= > c = k^z

a , b and c are in G.P .

So : a c = b²

= > k^(x) . k^(z) = ( k^(y) )²

= > k^(x+z) = k^( 2y)

Comparing the powers :

x + z = 2 y

Hence x , y and z are in A.P [ Proved ]