Question

If $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ is the G.M. between two numbers $a$ & $b$, then the value of $n$ is

• A. 0
• B. 1
• C. 1/2
• D. none of these

Answer 1

Answer: (C)

1/2

$Answer:OptionCiscorrect.\frac{a^n+b^n}{a^{n-1}+b^{n-1}}=GM=\sqrt{ab}=a^{1/2}{b}^{1/2}Rearranging,a^n+b^{n}space=a^{1/2}{b}^{1/2}\times (a^{n-1}+b^{n-1})=a^{n-\left(1/2\right)}\times b^{1/2}+b^{n-\left(1/2\right)}\times a^{1/2}EquatingpowersofLHS\&RHS,weget,n-\frac{1}{2}=0Hence,n=\frac{1}{2}$