Is the Calculation of Arithmetic Means Between Two Numbers Always Intuitive?

[ermac]

Homework Statement

A question gives the problem find the two arithmetic means between 4 and 19.
The answer is 9 and 14.

Homework Equations

(a₁+a₂+a₃+a_n)/n

The Attempt at a Solution

Logic would dictate that the arithmetic mean would be adding 4 and 19 then dividing by two. Leaving the supposed answer to be 11 and a half.


This is for an academic team, so a step by step answer would be appreciated so that we may learn how to do it later.

 

[statdad]

You are on the wrong track (in my opinion). You are thinking in terms of the statistical arithmetic mean: there is only one of those between 4 and 19. I'm guessing the writer of the problem intended you to treat the given numbers as terms in an arithmetic sequence and find two terms (the new terms are the arithmetic means) that fall between them in the sequence.

So what would you try for that?

 

[HallsofIvy]

I agree completely with stat dad. Let d be the "common difference" in the arithmetic sequence. Then we have 4, 4+ d, 4+ 2d, and 4+ 3d= 19.