16, 23, 30, 37, 44
We can note from the sequence that every number is the previous one plus 7, then the recursive formula will be.
[tex]a_n=a_{n-1}+7[/tex]for all n greater or equal that 2 because the first term a1=16. Now let's deduce the explicit formula
[tex]a_1=16[/tex][tex]a_2=a_1+1(7)[/tex][tex]a_3=30=16+2(7)=a_1+2(7)[/tex]at this point we can see the pattern, for the nth term, you add to the first term 7 multipied by (n-1), then the explicit formula is
[tex]a_n=16+(n-1)7[/tex]simplifying
[tex]a_n=9+7n[/tex]