Question

In G.P there are 'n' terms between a and b then find common ratio.

Answer 1

$\textbf{To find:}$

$\text{Common ratio of the G.P}$

$\textbf{Solution:}$

$\text{Let t_1,t_2,t_3.......t_n be the n terms between a and b}$

$\text{Let r be the common ratio}$

$\text{Then,}$

$t_1=a\,r$

$t_2=a\,r^2$

.

.

.

$t_n=a\,r^n$

$b=a\,r^{n+1}$

$\implies\,r^{n+1}=\dfrac{b}{a}$

$\implies\bf\,r=(\dfrac{b}{a})^{\frac{1}{n+1}}$

$\therefore\textbf{Common ratio of the G.P is \bf\,(\dfrac{b}{a})^{\frac{1}{n+1}} }$

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