Provide 2 methods of finding variable x is the terms 1,6x+2,13,19,..are terms of an a.p.

If the given series it's an arithmetical progression, that
means that each term, beginning from the second one, is the sum between previous term
and a constant amount, called common difference.

We can
find the ratio in this
way:

19=13+d

19-13=d

d=6

Based
on this rule, we can write the term 6x+2 =
1+d

6x+2=1+6

6x = 7 -
2

x = 5/6

Another way of
solving the problem would be to consider the
term

(6x+2)=(1+13)/2.

6x+2=7

6x=7-2

6x=5

x=5/6

Both
ways, we've get the same value for the variable x, namely x =
5/6.