Question

If the sequence $\left\{s_n\right\}$ is a geometric progression and $s_2{s}_{11}=s_p{s}_8$ , then what is the value of p?

• A. 1
• B. 3
• C. 5
• D. Can not be determined

Answer 1

The correct option is C 5

We know that, $n^{th}$ term of GP is $a\ast r^{n-1}$

So, $s_2=a{r}^{2-1}=ar$

$s_{11}=a{r}^{11-1}=a\ast r^{10}$

$s_8=a{r}^{8-1}=a\ast r^7$

$s_p=a{r}^{p-1}$

Since, $s_2{s}_{11}=s_p{s}_8$

$\Rightarrow s_p=\frac{s_2{s}_{11}}{s_8}\Rightarrow a{r}^{p-1}=\frac{a{r}^{10}ar}{a{r}^7}\Rightarrow r^{p-1}=r^{10+1-7}\Rightarrow p=10+1-7+1=5$