1) Write the first 4 elements of the sequence: (n+1)/(3n-1)

I got -1,1,3/5,1/2

not quite
2) Find a formula for the nth term of the sequence: 0,-1,0,1,0,-1,0,1,0,-1,0,1 -------- I got an= sin (nn)

If n starts at 1, then $\displaystyle -\sin[(n-1)\frac{\pi}{2}]$

3) Find limit of sequence if it converges:

an = 3-8n+4n^4/(3n^4+9n^3-2) -------- I got 4/3

good
4) Find limit of sequence if it converges; an = (3/n) subscript(3/n) --- I got 0.

I dont understand your language
5) Find limit of sequence if it converges; an= 5+ (-1)^n / 5 ---- I got 1

Diverges
6) Determine if the sequnce is decreasing/non-decreasing/bound/unbounde… :

an = (4n+1)/(n+1) ----- I got nondecreasing, bounded

If the answers aren't right, could someone explain/show what the correct answer is?