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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 p is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
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)`.
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