Chapter 12.2, Problem 82PE

The arithmetic mean (average) of two numbers c and d is given by $\bar{x}=\frac{c+d}{2}$ . The value $\bar{x}$ isequidistant between c and d, so the sequence c, $\bar{x}$ , dis an arithmetic sequence. Inserting k equallyspaced 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.

82. Insert four arithmetic means between 19 and 64.