Chapter 12.4, Problem 38E

To determine

To form an arithmetic sequence that has five arithmetic means between $-11$ and $19$ .

Answer to Problem 38E

The sequence is $-11$ , $-6$ , $-1$ , $4$ , $9$ , $14$ , $19$ .

Explanation of Solution

Given information:

To form an arithmetic sequence that has five arithmetic means between $-11$ and $19$ .

Calculation:

Find the common difference $d$ .

The first term of the sequence is $a=-11$ and seventh term is $a_7=19$ .

The nth term of the arithmetic sequence is given by:

  $a_n=a+\left(n-1\right)d$

Substitute the above values with $n=7$ .

  $\begin{array}{c}19=-11+\left(7-1\right)d\\ 19+11=6d\\ d=\frac{30}{6}\\ d=5\end{array}$

Therefore, second term is $a_2=a+d=-11+5=-6$

Third term is $a_3=a_2+d=-6+5=-1$

Fourth term is $a_4=a_3+d=-1+5=4$

Fifth term is $a_5=a_4+d=4+5=9$

Sixth term is $a_6=a_5+d=9+5=14$ .

Hence, the sequence is $-11$ , $-6$ , $-1$ , $4$ , $9$ , $14$ , $19$ .