Chapter 11, Problem 18SGR

To determine

Find the 3 arithmetic means between 72 and 24

Answer to Problem 18SGR

The 3 arithmetic means are $60,48,36$

Explanation of Solution

Given:

Find the three arithmetic means between 72 and 24

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: $a_1=72\text{and}{a}_5=24;\text{find}{a}_2,a_3,a_4$

  $\begin{array}{l}{a}_1=72\text{and}{a}_5=24,\text{find}d\\ a_n=a_1+(n-1)·d\\ a_5=a_1+(5-1)·d\\ 24=72+4d\\ 24-72=72-72+4d\\ 4d=-48\\ \frac{4d}{4}=\frac{-48}{4}\\ d=-12\end{array}$

  $\begin{array}{l}{a}_1=72\text{and}d=-12,\text{find}{a}_2,a_3,a_4\\ a_2=a_1+d=72-12=60\\ a_3=a_2+d=60-12=48\\ a_4=a_3+d=48-12=36\end{array}$

Thus, the 3 arithmetic means are $60,48,36$