Use number sentences to describe the rule and the n term of the following pattern: 5; 9; 13; 17; ...; n

    The difference between consecutive terms is $9-5=4$, $13-9=4$. The rule is to **add 4 to the previous term**.

    This is an arithmetic sequence with first term $a_1=5$ and common difference $d=4$.  
    The formula for the $n$-th term is $T_n = a_1 + (n-1)d$.
    $$
    T_n = 5 + (n-1)4
    $$
    $$
    T_n = 5 + 4n - 4
    $$
    $$
    T_n = \boxed{\textbf{4n + 1}}
    $$