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Question

If a,a1,a2,.....a2n,b are in A.P.,
a,g1,g2,.....g2n are in G.P
and a,h,b are in H.P then:
a1+a2ng1g2n+a1+a2n1g1g2n1+.....+an+an+1gngn+1=

A
2nh
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B
nh
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C
nh
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D
2nh
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Solution

The correct option is D 2nh
a,a1,a2,.........,a2n,b xh=1a+1b
a1+a2n(2n+1)(a+h)(2n+1)=a+b
Similarity, $a_{2}+a_{2n-1}=a+b
an+an+1=a+b
a,a1,a2,..........a2n1b
a1=(a2n)12n+1 a2n(b2na)12n+1
a1a2=ab
Similarity
a2a2n1=ab
anan+1=ab
a1+a2na1a2n+a2+a2n1a2a2n1+...........+an+an+1anan+1
a+bab+a+bab+...........a+bab=n(1a+1b)=2nb












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