Question

In Illustration 6, which one of the following statement is correct ?
A. `A_(1)gtA_(2)gtA_(3)gt . . .`
B. `A_(1)ltA_(2)ltA_(3) . . .`
C. `A_(1)gtA_(3)gtA_(5)gt. . .andA_(2)ltA_(4)ltA_(6)lt`
D. `A_(1)ltA_(3)ltA_(5) lt. . .andA_(2)gtA_(4)gtA_(6)gt . . .`

Answer 1

Correct Answer - A
We have, `A_(1)gtG_(1)gtH_(1)`
It is given that `A_(2)andH_(1)andA_(1)gtH_(1)`.
`:." "A_(1)gtA_(2)gtH_(1)" "{:[(because"Arithmetic mean lies"),("between the numbers")]:}`
`A_(3)` is the A.M. of `A_(2)andH_(2)andA_(2)gtH_(2)`.
`:." "A_(2)gtA_(3)gtH_(2)" "{:[(because"Arithmetic mean lies"),("between the numbers")]:}`
Hence, `A_(1)gtA_(2)gtA_(3)gt . . . . . .`