Chapter 11.3, Problem 3ST

(a)

To determine

To calculate:

The one arithmetic mean of the following each pair:

  $-2,10$

Answer to Problem 3ST

The one arithmetic means between $-2$ and $10$ is $4$

Explanation of Solution

Given information:

  $-2,10$

Calculation:

Need to determine one arithmetic mean between $-2$ and $10$ :

  $\begin{array}{l}n=1\\ a_1=-2\\ a_3=10\end{array}$

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

  $\begin{array}{l}d=\frac{a_3-a_1}{n+1}\\ d=\frac{10+2}{1+1}\\ d=\frac{12}{2}\\ d=6\end{array}$

Now, get that there is common difference of $6$ . Now, one term between $-2$ and $10$ are:

  $a_2=a_1+d=-2+6=4$

(b)

To determine

To calculate:

The two arithmetic means of the following each pair:

  $-2,10$

Answer to Problem 3ST

The two arithmetic means between $-2$ and $10$ are $2$ and $8$

Explanation of Solution

Given information:

  $-2,10$

Calculation:

Need to determine two arithmetic means between $-2$ and $10$ :

  $\begin{array}{l}n=2\\ a_1=-2\\ a_4=10\end{array}$

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

  $\begin{array}{l}d=\frac{a_4-a_1}{2+1}\\ d=\frac{10+2}{2+1}\\ d=\frac{12}{3}\\ d=4\end{array}$

Now, get that there is common difference of $4$ . Now, one term between $-2$ and $10$ are:

  $\begin{array}{l}{a}_2=a_1+d=-2+4=2\\ a_3=a_2+d=2+6=8\end{array}$