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Question

The value of n for which xn+1+yn+1xn+yn is the geometric mean of x and y is

A
n=12
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B
n=12
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C
n=1
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D
n=1
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Solution

The correct option is A n=12
Given, xn+1+yn+1xn+yn=xy .......... Geometric mean

xn+1+yn+1=xy(xn+yn)

xxnxnx12y12=ynx12y12yyn

xn+12(x12y12)=yn+12(x12y12)
(xy)n+12=1
(xy)n+12=(xy)0

n+12=0n=12

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