SOLUTION: Insert 2 arithmetic means between 10 and 37.

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Question 1185813: Insert 2 arithmetic means between 10 and 37.
Answer by ikleyn(52790) About Me  (Show Source):
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Imagine yourself working on the number line.


When you insert two arithmetic means between the points 10 and 37,  you get 3 (three) intervals

of equal length on the segment  [10,37],  whose length is 37-10 = 27 units.



These three segments have the same length, so the length of each small segment is  27/3 = 9 units.



This length of small segments is nothing else as the common difference of the arithmetic progression.



HENCE, you have an arithmetic progression  10, 19, 28, 37,



and the inserted arithmetic means are the points (the values)  19 and 28.

Solved.