If (x-2) , 7 , (2x+1) are terms of an A.P , find x.

Given that:

(x-2) , 7 ,
(2x+1) are terms of an arithmetical progression.

Then, we
will assume that the common difference is r .

Then we know
that:

7 = (x-2) + r

==>
7 - r = x-2

==> x = 9 - r
................(1)

Also, we know
that:

2x+1 = 7 + r

==>
2x = 6 + r ..................(2)

Now we will add (1) and
(2).

==> 3x =
15

==> x = 15/3 = 5

To
check:

5 -2 = 3

2x +1 = 2(5) +
1 = 11

==> 3, 7, 11  are terms of an A.P where the
common difference is r = 4

==> x =
5