So you are given a recursive series, which is an equation that writes itself. Now we want to create a explicit rule. Explicit rule is a pattern that uses our first term and add our common difference. So it gives us our first term. 
Lets find the second term of the recursive series.
a_2 = -3 +7 = 4
So it is increasing by 7
So our explicit rule is:
a_n = -3 + 7(n-1)
Lets find the second term of the recursive series.
a_2 = -3 +7 = 4
So it is increasing by 7
So our explicit rule is:
a_n = -3 + 7(n-1)