Setting 1+19k = (1-k)+2(n-1)k and re-writing:
        1+19k = 1-3k+2nk   
          19k = -3k+2nk      << subtracted 1 from both sides
          19  = -3+2n        << divided both sides by k
          22  = 2n           << added 3 to both sides
          11  = n            << divided both sides by 2

Number of terms is the same, as the number of terms in the sequence


    -1, 1, 3, 5, . . . , 19.



Even if you know nothing about arithmetic progressions, and even if you are 2-nd grade student, 

you can solve this problem and answer this question by writing all the terms of the sequence in a row and counting them.



But if you are a bit more advanced thinker, you may figure out that the number of gaps between 1 an 19 is

      =  = 9;



Hence, the number of term in the sequence  1, 3, 5, . . . , 19  is  10;



Then joining the term  {-1},  you get that the number under the problem's question is  10 + 1 = 11.    ANSWER