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Question

If x, y and z are pth,qth and rth terms respectively of an A.P. and also of a G.P., then xyzyzxzxy is equal to

A
xyz
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B
0
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C
1
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D
None of these
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Solution

The correct option is C 1
Given that x, y, z are the pth,qth and rth terms of an A.P.
x=A+(p1)D
y=A+(q1)D
z=A+(r1)D
xy=(pq)D
yz=(qr)D
zx=(rp)D
where A is the first term and D is the common difference.

Also, x, y, z are the pth,qth and rth terms of a G.P.
x=aRp1, y=aRq1, z=aRr1
xyzyzxzxy=(aRp1)yz(aRq1)zx(aRr1)xy =(aR)=1

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