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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

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

m = 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 m 1 , m 2 , ... , m k are equally spaced between a and b so that

a , m 1 , m 2 , ... , m k , b

is an arithmetic sequence, then m 1 , m 2 , ... , m k are called k arithmetic means between a and b .

(a) Insert two arithmetic means between 10   and   18 .

(b) Insert three arithmetic means between 10   and   18 .

(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?

To determine

a)

To find:

Two arithmetic means between 10 and 18.

Explanation

Given:

Numbers 10 and 18.

Approach:

Since the numbers 10 and 18 and the two arithmetic means form an arithmetic sequence so take 10 as the first term and d as the unknown common difference and express 18 in terms of 10 and d.

Calculation:

Since the two arithmetic means form an arithmetic sequence together with 10 and 18. So we can write this arithmetic sequence as 10,10+d,10+2d,10+3d where d is the common difference of this sequence.

10+d,10+2d are the arithmetic means.

Hence,

To determine

b)

To find:

Three arithmetic means between 10 and 18.

To determine

c)

To find:

How many arithmetic means must be inserted between 100and300 to give the progression of daily doses, and what are these means?

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