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I am not sure if my understanding of subsequence is right. For example I have sequence {x} from n=1 to infinity. Subsequence is when

A) I chose for example every third term of that sequence so from sequence 1,2,3,4,5,6,7,... I choose subsequence 1,4,7...?

B) Or subsequence is when I chose for example only first five terms so from sequence 1,2,3,4,5,6,7... I choose subsequence 1,2,3,4,5...?

I have this problem because {x} from n=1 to infinity is non-convergent sequence and I want to know if subsequence of non-convergent sequence is also always non-convergent like in A) or we can make convergent subsequence from non-convergent sequence B).

BY THE WAY SEQUENCE 1,2,3,4,5 IS CONVERGENT, RIGHT? :D