The arithmetic mean (or average) of two numbers a and b is
a + b
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,
a, m₁, M₂,..., mk, b
is an arithmetic sequence, then m₁, m₂, ..., mk are called k arithmetic means between a and b.
(a) Insert two arithmetic means between 15 and 23.
(b) Insert three arithmetic means between 15 and 23.
.., mk are equally spaced between a and b so that
(c) Suppose a doctor needs to increase a patient's dosage of a certain medicine from 100 mg to 450 mg per day in five equal steps. How many arithmetic means must be inserted between 100 and 450 to give the progression of daily doses?
What are these means? (Enter your answers as a comma-separated list.)
Answer rating: 100% (QA)
a a 15 b 23 Calculation of the common difference d between the means d b a 2 1 23 15 3 8 3 m1 aView the full answer