Question

If $x_1,x_2,x_3,x_4$ are in G.P., then its common ratio is-

• A. $(\frac{ar}{cp}{)}^{1/4}$
• B. $(\frac{cr}{ap}{)}^{1/3}$
• C. $\sqrt{\frac{cr}{ap}}$
• D. $\sqrt{\frac{ap}{bq}}$

Answer 1

Answer: (A)

$(\frac{ar}{cp}{)}^{1/4}$

$x_1+x_2=-b/a,x_1{x}_2=c/a$,
$x_3+x_4=-q/p,x_3{x}_4=r/p$,
$x_2=x_1{r}^{\prime },x_3=x_1{r}^{\prime 2},x_4=x_1{r}^{\prime 3}$
$x_1{x}_2=x_1^2{r}^{\prime }=c/a.....\left(i\right)$
$x_3{x}_4=x_1^2{r}^{\prime }5=r/p....\left(ii\right)$
Dividing (ii) by (i) $r^{\prime 4}=\frac{ra}{pc}\Rightarrow (\frac{ra}{pc}{)}^{1/4}=r^{\prime }$