A) A sequence is a list of terms . There are main 2 types of sequence one is convergent and the other one is divergent. Convergent sequence is when through some terms you achieved a final and constant term as n approaches infinity . Divergent sequence is that in which the terms never become constant they continue to increase or decrease and they approach to infinity or -infinity as n approaches infinity. The sequence could be presented as the function and if we would put x values we would get different terms of f(x). let say n is equal to x and the terms in sequence is equal to f(x).we increase the x values and take that to infinity if the f(x) values would become constant to a finite value, as x approach infinity then the sequence of the terms is said to be convergent . But if the f(x) values continue to increase or decrease and went towards infinity or -infinity then the sequence is said to be divergent.
B)Now series is different from sequence . The meaning of the series convergence and divergence could be very different as of the sequences. If the partial sums of the terms become constant then the series is said to be convergent but if the partial sums go to infinity or -infinity then the series is said to be divergent.As n approaches infinity then if the partial sum of the terms is limit to zero or some finite number then the series is said to be convergent for examples we could take an example of the geometric series there is (r^(n)) which is constantly multiplying to the first term. Now if A=5, R is smaller than 1 and let say it is 0.5then let say (5,2.5,1.25…) it will continue to decrease to zero (as when n approaches infinity term would become ) but the term reaching zero would not give us the answer but actually it is the sum of the terms which is becoming constant to 10 . so the series converges to 10.so the Sn (partial sums limits to 10) . But if R is 2 so the partial sums would continue to increase to infinity and this means that the series is divergent.