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

Question 975018: Insert 2 arithmetic means between x+y and 4x-2y

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
Insert two arithmetic means between -7 and... (answered by Edwin McCravy)

insert 3 arithmetic means between -6 and 2 (answered by Alan3354)

insert 2 arithmetic means between 3/5 and 5/3 (answered by MathLover1)

insert seven arithmetic means between 2 and... (answered by ikleyn)

Insert 2 arithmetic means between 10 and 37. (answered by ikleyn)

Insert 4 arithmetic means between -11. And... (answered by richwmiller)

Insert 4 arithmetic means between -11 and... (answered by richwmiller)

insert four arithmetic means between 68 and... (answered by richwmiller)

insert 4 arithmetic means between -11 and... (answered by richwmiller)