need to calculate sum of 3 consecutive terms of arithmetic sequence x+4,3x,13x-2

If  x+4,3x,13x-2, are the consecutive terms of an
arithmetical progression, then the middle term is the arithmetical mean of x+4 and
13x-2.

3x=(x+4+13x-2)/2

3x =(14x-2)/2

By
cross multiplying, the result will
be:

6x=14x-2

We'll subtract
14x both sides:

6x-14x =
-2

-8x = -2

We'll divide by
-8:

x = 2/8

x =
1/4

The consecutive terms
are:

x + 4 = 1/4 + 4 = (1+16)/4 =
17/4

3x = 3/4

13x - 2 = 13/4 -
2 = (13-8)/4 = 5/4

The sum of terms
is:

x + 4 + 3x + 13x - 2 = 17x +
2

17x + 2 = 17/4 + 2

17x + 2 =
(17+8)/4

x + 4 + 3x + 13x - 2 = 17x + 2 =
25/4