$(7)$ Determine whether the sequence converges or diverges. If it converges, find the limit$.$

$($a$)a_n=\frac{3^n}{4^n}$

$($b$)b_n=sin(n)$

$($c$)c_n=\frac{(-1{)}^{n}3n^3}{9n^5+7}$

$($d$)d_n=\frac{(lnn{)}^2}{n}$