Chapter 11.2, Problem 37PPS

To determine

Find the five arithmetic means between − 12 and − 66.

Answer to Problem 37PPS

The five arithmetic means are $-21,-30,-39,-48,-57$

Explanation of Solution

Given:

Find the three arithmetic means between− 12 and − 66..

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: $a_1=-12\text{and}{a}_7=-66$; find $a_2,a_3,a_4,a_5,a_6$

  $\begin{array}{l}{a}_1=84\text{and}{a}_7=39,\text{find}d\\ a_n=a_1+(n-1)·d\\ a_7=a_1+(7-1)·d\\ -66=-12+6d\\ -66+12=-12+12+6d\\ 6d=-54\\ \frac{6d}{6}=\frac{-54}{6}\\ d=-9\end{array}$

  $\begin{array}{l}{a}_1=-12\text{and}d=-9,\text{find}{a}_2,a_3,a_4,a_5,a_6\\ a_2=a_1+d=-12-9=-21\\ a_3=a_2+d=-21-9=-30\\ a_4=a_3+d=-30-9=-39\\ a_5=a_4+d=-39-9=-48\\ a_6=a_5+d=-48-9=-57\end{array}$

Thus, the five arithmetic means are $-21,-30,-39,-48,-57$