Question

In Illustration 6, which one of the following statement is correct ?
A. `H_(1)gtH_(2)gtH_(3)gt . . .. `
B. `H_(1)ltH_(2)ltH_(3)lt . . .. `
C. `H_(1)gtH_(3)gtH_(5)gt . . .. andH_(2)ltH_(4)ltH_(6)lt . . ..`
D. `H_(1)ltH_(3)ltH_(5)lt . . .. andH_(2)gtH_(4)gtH_(6)gt . . ..`

Answer 1

Correct Answer - B
We have,
`A_(1)gtG_(1)gtH_(1)`
`H_(2)` is the harmonic mean of `A_(1)andH_(1)andA_(1)gtH_(1)`.
`:." "A_(1)gtH_(2)gtH_(1)" "{:[(because"Harmonic mean lies"),("between the numbers")]:}`
`H_(3)` is the Harmonic mean of `A_(2)andH_(2)andA_(2)gtH_(2)`
`:." "A_(2)gtH_(3)gtH_(2)" "{:[(because"Harmonic mean lies"),("between the numbers")]:}`
Similarly, we have
`A_(3)gtH_(4)gtH_(3),A_(4)gtH_(5)gtH_(4) . . . .`
Hence, `H_(1)ltH_(2)ltH_(3),A_(4) . . .. .`