Chapter 11.2, Problem 23WE

(a)

To determine

To calculate:

The two arithmetic means of the following each pair:

  $-27,33$

Answer to Problem 23WE

The two arithmetic means between $-27$ and $33$ are $-15$ and $3$

Explanation of Solution

Given information:

  $-27,33$

Calculation:

Need to determine three arithmetic means between $-27$ and $33$ :

  $\begin{array}{l}n=2\\ a_1=-27\\ a_4=33\end{array}$

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:

  $\begin{array}{l}d=\frac{a_4-a_1}{n+1}\\ d=\frac{33+27}{2+1}\\ d=\frac{60}{3}\\ d=20\end{array}$

Now, get that there is common ratio of $20$ . Now, two terms between $-27$ and $33$ are:

  $\begin{array}{l}{a}_2=a_1+d=-27+20=-7\\ a_3=a_2+d=-7+20=13\end{array}$

(b)

To determine

To calculate:

The three arithmetic means of the following each pair:

  $-27,33$

Answer to Problem 23WE

The three arithmetic means between $-27$ and $33$ are $-12,3$ and $18$

Explanation of Solution

Given information:

  $-27,33$

Calculation:

Need to determine three arithmetic means between $-27$ and $33$ :

  $\begin{array}{l}n=3\\ a_1=-27\\ a_5=33\end{array}$

That means need to determine the value of $a_2,a_3,a_4$ between the given sequences. By using the common ratio, these values are to be calculated as:

  $\begin{array}{l}d=\frac{a_5-a_1}{n+1}\\ d=\frac{33+27}{3+1}\\ d=\frac{60}{4}\\ d=15\end{array}$

Now, get that there is common ratio of $15$ . Now, two terms between $-27$ and $33$ are:

  $\begin{array}{l}{a}_2=a_1+d=-27+15=-12\\ a_3=a_2+d=-12+15=3\\ a_4=a_3+d=3+15=18\end{array}$

(c)

To determine

To calculate:

The four arithmetic means of the following each pair:

  $-27,33$

Answer to Problem 23WE

The four arithmetic means between $-27$ and $33$ are $-15,-3,9$ and $21$

Explanation of Solution

Given information:

  $-27,33$

Calculation:

Need to determine four arithmetic means between $-27$ and $33$ :

  $\begin{array}{l}n=4\\ a_1=-27\\ a_6=33\end{array}$

That means need to determine the value of $a_2,a_3,a_4,a_5$ between the given sequences. By using the common ratio, these values are to be calculated as:

  $\begin{array}{l}d=\frac{a_6-a_1}{n+1}\\ d=\frac{33+27}{4+1}\\ d=\frac{60}{5}\\ d=12\end{array}$

Now, get that there is common ratio of $12$ . Now, two terms between $-27$ and $33$ are:

  $\begin{array}{l}{a}_2=a_1+d=-27+12=-15\\ a_3=a_2+d=-15+12=-3\\ a_4=a_3+d=-3+12=9\\ a_5=a_4+d=9+12=21\end{array}$