Question

The two geometric means between the numbers 1 and 64 are

• A. 1 and 64
• B. 4 and 16
• C. 2 and 16
• D. 8 and 16

Answer 1

The correct option is B

4 and 16

(b) 4 and 16

Let the two G.M. s between 1 and 64 and $G_1$ and $G_2$.

Thus, $1,G_1,G_2$ and 64 are in G.P.

$64=1\times r^3$

$\Rightarrow r=\sqrt[3]{364}$

$\Rightarrow r=4$

$\Rightarrow G_1=ar=1\times 4=4$

And $G_2=a{r}^2=1\times 4^2=16$

Thus, 4 and 16 are the required G.M.s.