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+1−an+1/2b1/2+bn+1−a1/2bn+1/2=0 ⇒(an+1/2−bn+1/2)(a1/2−b1/2)=0 ⇒(an+1/2−bn+1/2)=0(∵a≠b⇒a1/2≠b1/2) ⇒(ab)n+1/2=1=(ab)o⇒n+12=0⇒n=−12.