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.

Options

A. 0
B. 1
C. -1
D. none of these

Answer

B

Explanation

Since `(a^(n)+b^(n))/(a^(n-1)+b^(n-1))` is Am of a and b.
`:." "(a^(n)+b^(n))/(a^(n-1)+b^(n-1))=(a+b)/(2)`
`rArr" "2a^(n)+2b^(n)=a^(n)+b^(n)+ab^(n-1)+a^(n-1)b`
`rArr" "a^(n-1)(a-b)=b^(n-1)(a-b)`
`rArr" "((a)/(b))^(n-1)=1rArrn-1=0rArrn=1`
ALITER We have,
`(a^(n)+b^(n))/(a^(n-1)+b^(n-1))(a+b)/(2)`
`rArr" "(a^(n)+b^(n))/(a^(n-1)+b^(n-1))=(a+b)/(2)=(a^(1)+b^(1))/(a^(0)+b^(0))`
On comparing the two sides, we obtain n=0.