It is given that the AP consists of the terms 1 , 6x + 2 , 13 , 19 ...

As the consecutive terms of an AP have a common difference:

13 - 6x - 2 = 6x + 2 - 1

=> 11 - 6x = 6x +1

=> 12x = 10

=> x = 10 / 12

=> x = 5 / 6

Also, if we take three consecutive terms of an AP, the second term is equal to the average of the 1st and the 3rd terms.

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

=> 14 = 12x + 4

=> 10 = 12x

=> x = 10 / 12

=> x = 5/6

Therefore the required value of x is 5/6.