Given x ,4,y,12 the terms of an A.P. find x and y .

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We'll use the theorem of arithmetic mean to determine the terms of the arithmetic progression.

4 = (x+y)/2 => 8 = x+y (1)

y = (4+12)/2

y = 16/2

y = 8

We'll substitute y into (1):

8 = x+8

We'll subtract 8 both sides, to isolate x:

8-8 = x

x = 0

We'll verify if the terms x and y are the terms of the a.p. in this way:

x,4,y,12

4 - x = y - 4 = 12 - y = d - common difference

4 - 0 = 8 - 4 = 12 - 8 = d

4 =4 = 4 = d

The terms of the arithmetic progression are, whose common difference is d = 4 :

0 , 4 , 8 , 12 , ....

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