What is the geometric mean of the ratio of corresponding terms of two series where `G_(1)" and "G_(2)` are geometric means of the two series ?`

Options

A. `log G_(1)-logG_(2)`
B. `log G_(1)+logG_(2)`
C. `(G_(1))/(G_(2))`
D. `G_(1)G_(2)`

Answer

C

Explanation

Let series be a, `G_(1),b" and "a',G_(2),b'" so,"G_(1)sqrt(ab)" and "G_(2)=sqrt(a'b')`
Series formed by ratio of the corresponding terms are :
`(a)/(a'),(G_(1))/(G_(2)),(b)/(b').`
Geometric means of this series `=sqrt((a)/(a'),(b)/(b'))`
`=sqrt((ab)/(a'b'))=(sqrt(ab))/(sqrt(a'b'))=(G_(1))/(G_(2))`
So, geometric mean of the ratio of corresponding term of two series where `G_(1)` and `G_(2)` are geometric means of two series is `(G_(1))/(G_(2)).`