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Suppose p is the first of n(ngt1) arithm...

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 q is

A

`((n-1)ab)/(nb+a)`

B

`((n+1)ab)/(nb+a)`

C

`((n-1)ab)/(na+b)`

D

`((n-1)ab)/(na+b)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`
`(1)/(q)=(1)/(a)+D=(1)/(a)+((1)/(b)-(1)/(a))/(n+1)`
`implies q=(ab(n+1))/(a+bn)`.
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