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If (a^n+b^n)/(a^(n-1)+b^(n-1))is the A.M...

If `(a^n+b^n)/(a^(n-1)+b^(n-1))`is the A.M. between a and b, then find the value of n.

A

-1

B

0

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
c
Since , `(a+b)/2 = (a^(n)+b^(n))/(a^(n-1)+b^(n-1))`
` rArr (a+b) (a^(n-1)+b^(n-1))= 2 (a^(n)+b^(n))`
` rArr (ab^(n))/b + (ba^(n))/a= a^(n)+b^(n)`
` rArr a^(n) ((a-b)/a)= -b ^(n) ((b-a)/b)`
` rArr (a^(n))/(b^(n)) = a/b rArr n=1`
Alternate Method
By hit and trial method
If we put , n=1 , then ` (a^(1)+b^(1))/(a^(0)+b^(0) ) = (a+b)/2 `
Hence , n=1
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