Question

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

• A. 79
• B. 80
• C. 81
• D. 82

Answer 1

Answer: (C)

81

$\begin{array}{c}Let\frac{1}{3},G_1,G_2,G_3,G_4,G_5,243\to G.P,\\ r=commonratio,\\ a_n=a{r}^{n-1}\\ \Rightarrow a_7=243\\ \Rightarrow a{r}^{7-1}=243\\ \Rightarrow \left(\frac{1}{3}\right)r^6=243\\ r^6=729\\ \Rightarrow r^6={\left(3\right)}^6\\ \Rightarrow r=3\\ G_1=ar\\ \Rightarrow \frac{1}{3}\times 3=1\\ G_2=a{r}^2\\ \Rightarrow \frac{1}{3}{\left(3\right)}^2=3\\ Similarly,G_3=9,G_4=27,G_5=81\end{array}$