Chapter 12.2, Problem 81PE

The arithmetic mean (average) of two numbers c and d is given by $\bar{x}=\frac{c+d}{2}$ . The value $\bar{x}$ is equidistant between c and d, so the sequence c, $\bar{x}$ , d is an arithmetic sequence. Inserting k equally spaced values between c and d, yields the arithmetic sequence c, ${\bar{x}}_1,{\bar{x}}_2,{\bar{x}}_3,{\bar{x}}_4,\mathrm{...}{\bar{x}}_k$ , d. Use this information for Exercises 81−82.

81. Insert three arithmetic means between 4 and 28. (Hint: There will be a total of five terms. Writethe nth term of an arithmetic sequence with $a_1=4$ and $a_5=28$ , and then find $a_2,a_3$ , and $a_4$ .)