Given the terms:
(x-2) , 6,
(2x-3) are terms of an arithmetical progression.
Then, we
will assume that "r" is the common difference between
terms.
==> 6 = (x-2) +
r
==> x+r =
8.............(1)
==> (2x-3) = 6 +
r
==> 2x -r = 9
..............(2)
Now we will solve the system using the
elimination method.
We will add (1) and
(2).
==> 3x =
17
==> x =
17/3
==> r = 6- 11/3 =
7/3
==> (x-2) = 17/3 - 6/3 =
11/3
==> 6 =
6
==> 2x-3 = 34/3 - 9/3 =
25/3
==> 11/3, 6, 25/3 are terms of
A.P and the common difference is r = 7/3
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