Chapter 11.3, Problem 5ST

(a)

To determine

To calculate:

The one geometric means of the following:

  $2,16$

Answer to Problem 5ST

The one geometric means between $2$ and $16$ is

Explanation of Solution

Given information:

  $2,16$

Calculation:

Need to determine three geometric means between $2$ and $16$ :

  $\begin{array}{l}n=1\\ a=2\\ b=16\end{array}$

That means need to determine the value of $a_2$ between the given sequences. The geometric mean is given by the following expression:

  $G=\sqrt{ab}$

Now, put the given data:

  $\begin{array}{l}G=\sqrt{2\times 16}\\ G=\sqrt{32}\\ G=4\sqrt{2}\end{array}$

(b)

To determine

To calculate:

The two geometric means of the following each pair:

  $2,16$

Answer to Problem 5ST

The two geometric means between $2$ and $16$ are $4$ and $8$

Explanation of Solution

Given information:

  $2,16$

Calculation:

Need to determine three geometric means between $2$ and $16$ :

  $\begin{array}{l}n=2\\ a_1=2\\ a_4=16\end{array}$

That means need to determine the value of $a_2,a_3$ between the given sequences. By using the common ratio, these values are to be calculated as:

  $\begin{array}{l}{t}_4=t_1{r}^{\left(4-1\right)}\\ 16=\left(2\right)r^3\\ r^3=8\\ r=2\end{array}$

Now, get that there is common ratio of $2$ . Now, two terms between $2$ and $16$ are:

  $\begin{array}{l}{a}_2=a_1\times r=2\times 2=4\\ a_3=a_2\times r=4\times 2=8\end{array}$