SOLUTION: Insert 2 arithmetic means between x+y and 4x-2y

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Question 975018: Insert 2 arithmetic means between x+y and 4x-2y
Answer by Edwin McCravy(20056) About Me  (Show Source):
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Insert 2 arithmetic means between x+y and 4x-2y
Let the two arithmetic means be A and B, and the common difference be d.

Then the arithmetic sequence with 4 ternms goes:

x+y, A, B, 4x-2y

where

A = x+y+d
B = x+y+2d
B+d = 4x-2y

Substituting for B

x+y+2d+d = 4x-2y
x+y+3d = 4x-2y
    3d = 3x-3y
     d = x-y

A = x+y+d = x+y+x-y = 2x
B = x+y+2d = x+y+2(x-y) = x+y+2x-2y = 3x-y

x+y, 2x, 3x-y, 4x-2y

The two arithmetic means are 2x and 3x-y

Edwin