Question

If n GMs be inserted between $a$ and $b$, then the corresponding common ratio is

• A. ${\left(\frac{b}{a}\right)}^{1/n+1}$
• B. ${\left(\frac{a}{b}\right)}^{1/n+1}$
• C. ${\left(\frac{b}{a}\right)}^{1/n}$
• D. ${\left(\frac{a}{b}\right)}^{1/n}$

Answer 1

The correct option is A ${\left(\frac{b}{a}\right)}^{1/n+1}$

Let $G_1,G_2,.............G_n$ are the G.Ms inserted between $aandb$ and the common ration be ${}^{\prime }{r}^{\prime }$
$\Rightarrow G_1=ar,G_2=a{r}^2,.........G_n=a{r}^n,b=a{r}^{n+1}$
So using last term
$r^{n+1}=\frac{b}{a}\Rightarrow r={\left(\frac{b}{a}\right)}^{1/n+1}$
Hence, option 'A' is correct.