Chapter 11.2, Problem 26WE

(a)

To determine

To calculate:

The two arithmetic means of the following each pair:

  $0,20$

Answer to Problem 26WE

The two arithmetic means between $0$ and $20$ are $6.66$ and $13.32$

Explanation of Solution

Given information:

  $0,20$

Calculation:

Need to determine three arithmetic means between $0$ and $20$ :

  $\begin{array}{l}n=2\\ a_1=0\\ a_4=20\end{array}$

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:

  $\begin{array}{l}d=\frac{a_4-a_1}{n+1}\\ d=\frac{20-0}{2+1}\\ d=\frac{20}{3}\\ d=6.66\end{array}$

Now, get that there is common ratio of $6.66$ . Now, two terms between $0$ and $20$ are:

  $\begin{array}{l}{a}_2=a_1+d=0+6.66=6.66\\ a_3=a_2+d=6.66+6.66=13.32\end{array}$

(b)

To determine

To calculate:

The three arithmetic means of the following each pair:

  $0,20$

Answer to Problem 26WE

The three arithmetic means between $0$ and $20$ are $5,10$ and $15$

Explanation of Solution

Given information:

  $0,20$

Calculation:

Need to determine three arithmetic means between $0$ and $20$ :

  $\begin{array}{l}n=3\\ a_1=0\\ a_5=20\end{array}$

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:

  $\begin{array}{l}d=\frac{a_5-a_1}{n+1}\\ d=\frac{20-0}{3+1}\\ d=\frac{20}{4}\\ d=5\end{array}$

Now, get that there is common ratio of $5$ . Now, two terms between $0$ and $20$ are:

  $\begin{array}{l}{a}_2=a_1+d=0+5=5\\ a_3=a_2+d=5+5=10\\ a_4=a_3+d=10+5=15\end{array}$

(c)

To determine

To calculate:

The four arithmetic means of the following each pair:

  $0,20$

Answer to Problem 26WE

The four arithmetic means between $0$ and $20$ are $4,8,12$ and $16$

Explanation of Solution

Given information:

  $0,20$

Calculation:

Need to determine four arithmetic means between $0$ and $20$ :

  $\begin{array}{l}n=4\\ a_1=0\\ a_6=20\end{array}$

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:

  $\begin{array}{l}d=\frac{a_6-a_1}{n+1}\\ d=\frac{20-0}{4+1}\\ d=\frac{20}{5}\\ d=4\end{array}$

Now, get that there is common ratio of $4$ . Now, two terms between $0$ and $20$ are:

  $\begin{array}{l}{a}_2=a_1+d=0+4=4\\ a_3=a_2+d=4+4=8\\ a_4=a_3+d=8+4=12\\ a_5=a_4+d=12+4=16\end{array}$