Suppose p is the first of `n(ngt1)` arithmetic means between two positive numbers a and b and q the first of n harmonic means between the same two numbers.
The value of p is

Options

A. `(na+b)/(n+1)`
B. `(nb+a)/(n+1)`
C. `(na-b)/(n+1)`
D. `(nb-a)/(n+1)`

Answer

A

Explanation

For `ngt1`, we have `n+1gtn-1`
`implies (n+1)/(n-1)gt1 implies p((n+1)/(n-1))^(2)gtp" " [:.pgt0]".......(i)"`
Now, `p=a+d`
Since,a,p,b are in AP.
And `d=(b-a)/(n+1)`
`p=a+((b-a))/(n+1)=(na+b)/(n+1)`.