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Question

If a,a1,a2,,...,a2n,bare in arithmetic progression and a,g1,g2,..,g2n,bare in geometric progression and is the harmonic mean of a and b is


A

2nh

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B

n/h

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C

nh

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D

2n/h

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Solution

The correct option is D

2n/h


Explanation for the correct option:

Finding the value:

Given a,a1,a21,,a2n,bare in arithmetic progression so a1,a21,,a2n are AMs between a,b

so, a1+a2n=a2+a2n-1=a+b

Given a,g1,g2,..,g2n,bare in GP.

so g1g2n=g2g2n-1=gngn+1=ab

(a1+a2n)g1g2n+(a2+a2n-1)g2g2n-1+.............+(an+an+1)gngn+1=a+bab+a+bab+.....a+bab=na+bab=2nhwhereh=(2aba+b)

Hence, option (D)is the correct answer.


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