Question

one of the $5$ geometric means between $\frac{1}{3}$ and $243$ is

• A. 82
• B. 81
• C. 80
• D. 79

Answer 1

Answer: (B)

$a=\frac{1}{3},b=243,g_1,g_2,g_3,g_4,g_5$ are
$5$ geometric means $b=a{r}^6$
$243=\frac{1}{3}{r}^6$
$r=3$
$g_1=ar=1$
$g_2=a{r}^2=3$
$g_3=a{r}^3=9$
$g_4=a{r}^4=27$
$g_5=a{r}^5=81$