Question

Insert three geometric means between $\frac{1}{3}$ and 432. The three means are:

• A. 3, 9, 27
• B. 2, 12, 72
• C. 9, 27, 81
• D. 4, 24, 144

Answer 1

The correct option is B

2, 12, 72

Let $G_1$, $G_2$ and $G_3$ be the three geometric means.

then $\frac{1}{3}$, $G_1,G_2,G_3$, 432 is a G.P.

$a=\frac{1}{3},a{r}^4=432$

$\Rightarrow \frac{1}{3}.r^4=432$

$r^4=1296\Rightarrow r=6$

$\therefore G_1=ar=\frac{1}{3}\times 6=2$

$G_2=a{r}^2=\frac{1}{3}\times 36=12$

$G_3=a{r}^3=\frac{1}{3}\times 216=72$