Chapter 11, Problem 17SGR

To determine

Find the 4 arithmetic means between 12 and − 8.

Answer to Problem 17SGR

The 4 arithmetic means are $8,4,0,-4$

Explanation of Solution

Given:

Find the 4 arithmetic means between12 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:

Given:; $a_1=12\text{and}{a}_6=-8;\text{find}{a}_2,a_3,a_4,a_5$

  $\begin{array}{l}{a}_1=12\text{and}{a}_6=-8,\text{find}d\\ a_n=a_1+(n-1)·d\\ a_6=a_1+(6-1)·d\\ -8=12+5d\\ -8-12=12-12+5d\\ 5d=-20\\ \frac{5d}{5}=\frac{-20}{5}\\ d=-4\end{array}$

  $\begin{array}{l}{a}_1=12\text{and}d=-4,\text{find}{a}_2,a_3,a_4,a_5\\ a_2=a_1+d=12-4=8\\ a_3=a_2+d=8-4=4\\ a_4=a_3+d=4-4=0\\ a_5=a_4+d=0-4=-4\end{array}$

Thus, the 4 arithmetic means are $8,4,0,-4$