The two geometric means between the numbers 1 and 64 are: - Vidyadip

MCQ

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

4 and 16

Solution:

Let the two G.M.s between 1 and 64 be G₁ and G₂.

Thus, 1, G₁, G₂ and 64 are in G.P.

$64=1\times\text{r}^3$

$\Rightarrow\text{r}=\sqrt[3]{64}$

$\Rightarrow\text{r}=4$

$\Rightarrow\text{G}_1=\text{ar}=1\times4=4$

And, $\text{G}_2=\text{ar}^2=1\times4^2=16$

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

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