Chapter 11.2, Problem 6CYU

To determine

Find the three arithmetic means between − 4 and 8.

Answer to Problem 6CYU

The three arithmetic means are $-1,2,5$

Explanation of Solution

Given:

Find the three arithmetic means between− 4 and 8.

Concept Used:

Arithmetic mean (average) of n numbers is there sum divided by the n.

"Arithmetic means" means that a constant number is being added again and again to create a sequence.

Calculation:

The primary arithmetic mean is the midpoint between − 4 and 8

  $\frac{-4+8}{2}=\frac{4}{2}=2$

The arithmetic mean between the initial value − 4 and the midpoint 2 is

  $\frac{-4+2}{2}=\frac{-2}{2}=-1$

The arithmetic mean between the midpoint 2 and the final value 8 is

  $\frac{2+8}{2}=\frac{10}{2}=5$

  $\begin{array}{l}-4,\underrightarrow{?},\underrightarrow{?},\underrightarrow{?},8\\ -4,\underrightarrow{?},\frac{-4+8}{2},\underrightarrow{?},8\\ -4,\underrightarrow{?},,2,\underrightarrow{?},,8\\ -4,\frac{-4+2}{2},2,\frac{2+8}{2},8\\ -4,-1,2,5,8\end{array}$

Thus, the three arithmetic means are $-1,2,5$