DISCUSS: Arithmetic Means The arithmetic mean(or average) of two numbers is
Note that is the same distance from as from , so is an arithmetic sequence. In general, if are equally spaced between so that
is an arithmetic sequence, then are called arithmetic means between .
(a) Insert two arithmetic means between .
(b) Insert three arithmetic means between .
(c) Suppose a doctor needs to increase a patient’s dosage of a certain medicine from to per day in five equal steps. How many arithmetic means must be inserted between and to give the progression of daily doses, and what are these means?
Two arithmetic means between and
Numbers and .
Since the numbers and and the two arithmetic means form an arithmetic sequence so take as the first term and as the unknown common difference and express in terms of and .
Since the two arithmetic means form an arithmetic sequence together with and . So we can write this arithmetic sequence as where is the common difference of this sequence.
are the arithmetic means.
Three arithmetic means between and
How many arithmetic means must be inserted between to give the progression of daily doses, and what are these means?
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