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Chapter 22: Problem 672

Insert five arithmetic means between 13 and 31 .

Short Answer

Expert verified
The five arithmetic means between 13 and 31 are 16, 19, 22, 25, and 28.

Step by step solution

01

Determine the common difference between the arithmetic means.

By inserting five arithmetic means between 13 and 31, we are dividing the interval between them into six equal parts. To find the common difference (d) between the arithmetic means, we will subtract the smaller number from the larger number and divide the result by the total number of parts. So, the common difference (d) between the arithmetic means is: \(d = \frac{31 - 13}{6}\)
02

Calculate the common difference.

Now, let's calculate the common difference (d) as mentioned above: \(d = \frac{31 - 13}{6} = \frac{18}{6} = 3\) So, the common difference between the arithmetic means is 3.
03

Find the five arithmetic means.

To find the five arithmetic means, we will simply add the common difference (d) to the starting number (13) and repeat this process for each of the arithmetic means. First arithmetic mean: \(13 + 3 = 16\) Second arithmetic mean: \(16 + 3 = 19\) Third arithmetic mean: \(19 + 3 = 22\) Fourth arithmetic mean: \(22 + 3 = 25\) Fifth arithmetic mean: \(25 + 3 = 28\) So, the five arithmetic means between 13 and 31 are 16, 19, 22, 25, and 28.

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