Chapter 11.2, Problem 25WE

(a)

To determine

To calculate:

The two arithmetic means of the following each pair:

  $11,35$

Answer to Problem 25WE

The two arithmetic means between $11$ and $35$ are $19$ and $27$

Explanation of Solution

Given information:

  $11,35$

Calculation:

Need to determine three arithmetic means between $11$ and $35$ :

  $\begin{array}{l}n=2\\ a_1=11\\ a_4=35\end{array}$

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:

  $\begin{array}{l}d=\frac{a_4-a_1}{n+1}\\ d=\frac{35-11}{2+1}\\ d=\frac{24}{3}\\ d=8\end{array}$

Now, get that there is common ratio of $8$ . Now, two terms between $11$ and $35$ are:

  $\begin{array}{l}{a}_2=a_1+d=11+8=19\\ a_3=a_2+d=19+8=27\end{array}$

(b)

To determine

To calculate:

The three arithmetic means of the following each pair:

  $11,35$

Answer to Problem 25WE

The three arithmetic means between $11$ and $35$ are $17,23$ and $29$

Explanation of Solution

Given information:

  $11,35$

Calculation:

Need to determine three arithmetic means between $11$ and $35$ :

  $\begin{array}{l}n=3\\ a_1=11\\ a_5=35\end{array}$

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:

  $\begin{array}{l}d=\frac{a_5-a_1}{n+1}\\ d=\frac{35-11}{3+1}\\ d=\frac{24}{4}\\ d=6\end{array}$

Now, get that there is common ratio of $6$ . Now, two terms between $11$ and $35$ are:

  $\begin{array}{l}{a}_2=a_1+d=11+6=17\\ a_3=a_2+d=17+6=23\\ a_4=a_3+d=23+6=29\end{array}$

(c)

To determine

To calculate:

The four arithmetic means of the following each pair:

  $11,35$

Answer to Problem 25WE

The four arithmetic means between $11$ and $35$ are $15.8,20.6,25.4$ and $30.2$

Explanation of Solution

Given information:

  $11,35$

Calculation:

Need to determine four arithmetic means between $11$ and $35$ :

  $\begin{array}{l}n=4\\ a_1=11\\ a_6=35\end{array}$

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:

  $\begin{array}{l}d=\frac{a_6-a_1}{n+1}\\ d=\frac{35-11}{4+1}\\ d=\frac{24}{5}\\ d=4.8\end{array}$

Now, get that there is common ratio of $4.8$ . Now, two terms between $11$ and $35$ are:

  $\begin{array}{l}{a}_2=a_1+d=11+4.8=15.8\\ a_3=a_2+d=15.8+4.8=20.6\\ a_4=a_3+d=20.6+4.8=25.4\\ a_5=a_4+d=25.4+4.8=30.2\end{array}$