Find x and terms in the Arethmetical progression.2x , 17 , 3x-1

Given that 2x, 17,  3x-1 are terms is
A.P

Let us assume that the common difference is
r.

Then we know that:

17 = 2x
+ r ...........(1)

Also we know
that:

3x-1 = 17 + r

=>
-18 = -3x + r...........(2)

Let us solve the
system.

We will subtract (2) from
(1).

==> 35 =
5x

==> x = 35/5 =
7

Then x= 7

Now we
will substitute and determine the terms.

==> 14 ,
17, 20

Then the terms are : 14, 17, 20  and
the value of x = 7