I'm really stuck on these, any help is appreciated. In each of the following a sequence is defined recursively. Guess an explicit formula for the sequence, then use mathematical induction to prove the correctness of your formula. Sorry I had some font sizing issues. If you can just explain the first one, then I can probably figure out the other two. Thanks.

(a) csub(k) = 3csub(k- 1) + 1, for all integers k >= 2

c1 = 1

(b) gsub(k) = (gsub(k -1) ) / (gsub(k- 1) + 2) , for all integers k >= 2

g1 = 1

(c) psub(k) = psub(k -1) + 2 · 3^k, for all integers k >= 2

p1 = 2