Question

Find the median of the data $a,ar,a{r}^2$,......$a{r}^n$ where $n$ is an odd number.

• A. $a{r}^{\frac{n-1}{2}}$
• B. $\frac{a}{2}(1-r)r^{\frac{n+1}{2}}$
• C. $\frac{a}{2}(1+r)r^{\frac{n-1}{2}}$
• D. $\frac{a}{2}(1-r)r^{\frac{n-1}{2}}$

Answer 1

Answer: (A)

$a{r}^{\frac{n-1}{2}}$

n is odd

Median is $\left(\frac{n+1}{2}\right)th$ term

First term $=a$

Common ratio $=r$

$\therefore t_{\frac{n+1}{2}}=a{r}^{\frac{n+1}{2}-1}=a{r}^{\frac{n-1}{2}}$