Chapter 12.2, Problem 78E

DISCUSS: Arithmetic Means The arithmetic mean (or average) of two numbers a and b is

$m=\frac{a+b}{2}$

Note that m is the same distance from a as from b, so a, m, b is an arithmetic sequence. In general, if m₁, m₂, …, m_k are equally spaced between a and b so that

$a,m_1,m_2,\dots ,m_k,b$

is an arithmetic sequence, then m₁, m₂, …, m_k are called k arithmetic means between a and b.

1. (a) Insert two arithmetic means between 10 and 18.
2. (b) Insert three arithmetic means between 10 and 18.
3. (c) Suppose a doctor needs to increase a patient’s dosage of a certain medicine from 100 mg to 300 mg per day in five equal steps. How many arithmetic means must be inserted between 100 and 300 to give the progression of daily doses, and what are these means?