Chapter 11.2, Problem 24WE

(a)

To determine

To calculate:

The two arithmetic means of the following each pair:

  $15,45$

Answer to Problem 24WE

The two arithmetic means between $15$ and $45$ are $25$ and $35$

Explanation of Solution

Given information:

  $15,45$

Calculation:

Need to determine three arithmetic means between $15$ and $45$ :

  $\begin{array}{l}n=2\\ a_1=15\\ a_4=45\end{array}$

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:

  $\begin{array}{l}d=\frac{a_4-a_1}{n+1}\\ d=\frac{45-15}{2+1}\\ d=\frac{30}{3}\\ d=10\end{array}$

Now, get that there is common ratio of $10$ . Now, two terms between $15$ and $45$ are:

  $\begin{array}{l}{a}_2=a_1+d=15+10=25\\ a_3=a_2+d=25+10=35\end{array}$

(b)

To determine

To calculate:

The three arithmetic means of the following each pair:

  $15,45$

Answer to Problem 24WE

The three arithmetic means between $15$ and $45$ are $22.5,30$ and $37.5$

Explanation of Solution

Given information:

  $15,45$

Calculation:

Need to determine three arithmetic means between $15$ and $45$ :

  $\begin{array}{l}n=3\\ a_1=15\\ a_5=45\end{array}$

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:

  $\begin{array}{l}d=\frac{a_5-a_1}{n+1}\\ d=\frac{45-15}{3+1}\\ d=\frac{30}{4}\\ d=7.5\end{array}$

Now, get that there is common ratio of $7.5$ . Now, two terms between $15$ and $45$ are:

  $\begin{array}{l}{a}_2=a_1+d=15+7.5=22.5\\ a_3=a_2+d=22.5+7.5=30\\ a_4=a_3+d=30+7.5=37.5\end{array}$

(c)

To determine

To calculate:

The four arithmetic means of the following each pair:

  $15,45$

Answer to Problem 24WE

The four arithmetic means between $15$ and $45$ are $21,27,33$ and $39$

Explanation of Solution

Given information:

  $15,45$

Calculation:

Need to determine four arithmetic means between $15$ and $45$ :

  $\begin{array}{l}n=4\\ a_1=15\\ a_6=45\end{array}$

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:

  $\begin{array}{l}d=\frac{a_6-a_1}{n+1}\\ d=\frac{45-15}{4+1}\\ d=\frac{30}{5}\\ d=6\end{array}$

Now, get that there is common ratio of $6$ . Now, two terms between $15$ and $45$ are:

  $\begin{array}{l}{a}_2=a_1+d=15+6=21\\ a_3=a_2+d=21+6=27\\ a_4=a_3+d=27+6=33\\ a_5=a_4+d=33+6=39\end{array}$