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Question

If the geometric mean between a and b is an+1+bn+1an+bn, then the value of n is

A

1

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B

–1/2

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C
1/2
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D
2
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Solution

The correct option is B

–1/2


As given an+1+bn+1an+bn=(ab)1/2
(an+1an+1/2b1/2+bn+1a1/2bn+1/2=0
(an+1/2bn+1/2)(a1/2b1/2)=0
(an+1/2bn+1/2)=0 (aba1/2b1/2)
(ab)n+1/2=1=(ab)on+12=0n=12.

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