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Question

The arithmetic mean of a and b is an+bnan1+bn1. The value of n is


A

-1

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B

0

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C

1

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D

a

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Solution

The correct option is C

1


an+bnan1+bn1=a+b22an+2bn=(a+b)(an1+bn1)2an+2bn=an+ban1+abn1+bnan+bn=anba+abnban[1ba]=bn[ab1]an(aba)=bn(abb)an1=bn1(ab)n1=1(ab)n1=(ab)0 n1=0n=1


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