Question

The sum of the first ten terms of the geometric progression is $S_1$ and the sum of the next ten terms$\left({11}^{th}through{20}^{th}\right)$ is $S_2$ then the common ratio will be-

• A. $\pm 10\sqrt{\frac{S_1}{S_2}}$
• B. $\pm 10\sqrt{\frac{S_2}{S_1}}$
• C. $\pm \sqrt[10]{10\frac{S_2}{S_1}}$
• D. $\pm \sqrt[10]{10\frac{S_1}{S_2}}$

Answer 1

The correct option is C $\pm \sqrt[10]{10\frac{S_2}{S_1}}$

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

$S_1=a+ar+a{r}^2+......a{r}^9=\frac{a(r^{10}-1)}{(r-1)}{S}_2=a{r}^{10}+a{r}^{11}+a{r}^{12}+......a{r}^{19}{S}_2=r^{10}(a+ar+a{r}^2+......a{r}^9)S_2=r^{10}\frac{a(r^{10}-1)}{(r-1)}$

$\frac{S_2}{S_1}=r^{10}r=\pm \sqrt[10]{10\frac{S_2}{S_1}}$