Question

The two geometric means between the number $1$ 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 $16$

Explanation for correct option

Let the series is $1,ar,a{r}^2,64$

We know that a geometric series is of the form $a,ar,a{r}^2,a{r}^3,....$ where $a$is the first term and $r$ is the common difference

Now comparing with the given set we have

$a=1$ and $a{r}^3=64$

From $a{r}^3=64$ we get

$$\begin{gathered} \Rightarrow r^3=64 \\ \Rightarrow r=4 \end{gathered}$$

Therefore the second term is $ar=4$ and the third term is $a{r}^2=16$

Hence, the correct option is $\mathrm{Option}\left(\mathrm{B}\right)$