Please help me with this sequence question

Question

Please help me with this question

Determine whether the sequence converges or diverges. If it converges, find the limit. If it diverges write NONE.

Answer 1

3ⁿ⁺² = (3ⁿ)(3²)

3ⁿ⁺² = 9(3ⁿ)

a_n = 9(3ⁿ) / 4ⁿ

Does that converge? To what?

Answer 2

Consider a(n)=3^(n+2)/4^n=3^n*3^2/4^n=9*(3/4)^n. This is a geometric sequence in the form a(n)=a0*r^n. For the sequence to be convergent, |r|<1. Since r=3/4, then this sequence is convergent. Hence, the sequence would converge to:

lim n->∞ 9*(3/4)^n=0.