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Question

If mn and the sequences p,a,b,q and p,m,n,q each are in AP, then banm is ___.

A
23
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B
32
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C
1
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D
34
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Solution

The correct option is C 1
Given, p,a,b,q are in AP.
2a=p+b
2ab=p....(i)
Also, 2b=a+q.
2ba=q....(ii)

Also given that p,m,n,q are in AP.
2m=p+n
2mn=p...(iii)
Also, 2n=m+q.
2nm=q...(iv)

From eqns. (i) & (iii), we get
2ab=2mn....(v)
From eqns. (ii) & (iv), we get
2ba=2nm....(vi)

Subtracting (vi) from (v), we get

2ab(2ba)=2mn(2nm).
2ab2b+a=2mn2n+m
3a3b=3m3n
ba=nm
banm=1

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