For each sequence, write down the first $5$ terms and hence, or otherwise, express the sequence using a recursive formula.

1. $u_n=5n+3$

2. $v_n=9-\frac{n}{2}$

3. $p_n=2^n$

4. $q_n=n!$

(Note: $n!$ is called '$n$ factorial' and is defined as

so, for example, $4!=4\times 3\times 2\times 1$ and $1!=1$ )

After writing out the first $5$ terms, focus on what you need to do to the previous term to get to the next term each time.

For (a), notice that $13=8+5,$ and then $18=13+5,$ and so on.