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

If `(a^n+b^n)/(a^(n-1)+b^(n-1))` is the GM between a and b, then the v

1.	If `(a^n+b^n)/(a^(n-1)+b^(n-1))` is the GM between a and b, then the value of n is
Answer» We know that the AM between a and b is ` ((a +b))/2` `((a^(n) + b^(n))/( a^(n-1) +b^(n-1)))` is the AM between a and b ` Rightarrow ((a ^(n) +b^(n))/ (a^(n-1) +b^(n -1)) = (a+b)/2` ` Rightarrow 2a^(n) +2b^(n) = a^(n) +a^(n-1) b+b^(n-1) a+b^(n)` ` Rightarrow a^(n) +b^(n) a^(n-1) b+b^(n-1) a` ` Rightarrow a^(n) -a^(n-1) b=b^(n-1) a-b^(n) ` ` Rightarrow a^(n-1) (a-b) =b^(n-1) (a-b)` ` Rightarrow a^(n-1) =b^(n-1)` ` Rightarrow (a/b) ^(n-1) =1=(a/b)^(0) Rightarrow n-1 =0 Rightarrow n=1` Hence, the required value of n is 1.