Question

Find the three arithmetic means between 5 and 17.

Answer 1

d = difference between the means .
5 + d, 5 + 2d, and 5 + 3d.

Since the numbers are equally spaced from 17, we require 5 + 4d = 17. d = 3. :)
5 +3, 5+2(3), and 5 + 3(3)

Answer 2

If we let d be the difference between the arithmetic means, then we have that the arithmetic means are:

5 + d, 5 + 2d, and 5 + 3d.

However, since the numbers are equally spaced from 17, we require 5 + 4d = 17 <==> d = 3.

Thus, the numbers are:

5 + 3 = 8, 5 + 6 = 11, and 5 + 9 = 14.

I hope this helps!