a)For last term {an} of the sequence ,{an} less or equal to a constant, the sequence converged.If not,  the sequence diverged. The convergent sequence is like a road, which can arrive the destination(the final term), eventually, for example {0,0,0,0,0,0,0,0}. The divergent sequence is like you are traveling in the universe, you will not find the end(the final term approaches to infinity),for example,{1,-1,1,-1,1,-1,1,-1,1,-1}. Basically, the trent of convergent sequence will approach to a constant, the trent of divergent sequence approach to not approch to a constant(+-inifity or up and down).

b)For the convergent series, the sum of these term will approach to a constant.If not, the series will be divergent(+-inifity or up and down). So the idea is to calculate the sum of the series is close to a constant or not. So the convergent series is like a hungry breasts to approach to their preies,but they will not really catch the preies, for example , the sum of {1\n^2},n =[1,inifity). The divergent series is like the preies, run away from the breasts’ mouth,for example, the sum of{1\n},n=[1,inifity).