Question

In a G. P. of even number of terms the sum of all terms is $5$ times the sum of the odd term. Find the common ratio of the G.P.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (C)

$4$

$a,ar,a{r}^2,a{r}^3,a{r}^4,.......,a{r}^{2n-1}$

$S_{even}=5S_{odd}$

$S_{even}=\frac{a(r^{2n}-1)}{r-1}$

$S_{odd}=\frac{a(r^{2n}-1)}{r^2-1}$

$=>\frac{a(r^{2n}-1)}{r-1}=\frac{5\times a(r^{2n}-1)}{r^2-1}$

$=>r^{2n}-1=\frac{5(r^{2n}-1)}{r+1}$

$=>r=4$