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 num

Question

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 num

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)`

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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)`.

7 views Answered 2023-02-05 15:29