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 $64$
✓
$4$ and $16$
C
$2$ and $16$
D
$8$ and $16.$

✓

Answer

Correct option: B.

$4$ and $16$

Let the two $\text{G.M.s}$ between $1$ and $64$ be $G_1$ and $G_2$.
Thus, $1, \mathrm{G}_1, \mathrm{G}_2$ and $64$ are in $\text{G.P.}$
$64=1\times\text{r}^3$
$\Rightarrow\text{r}=\sqrt[3]{64}$
$\Rightarrow\text{r}=4$
$\Rightarrow\text{G}_1=\text{ar}=1\times4=4$
And, $\text{G}_2=\text{ar}^2=1\times4^2=16$
Thus, $4$ and $16$ are the required $\text{G.M.s.}$

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