a recursive rule for an arithmetic sequence is a1=−3; an=an−1+7.

what is the explicit rule for this sequence?

The first term is a(1) = -3
The recursive step is a(n) = a(n-1)+7 meaning "add 7 to each previous term to get the next term". This points us to the common difference d being 7

a1 = -3 
d = 7

an = a1 + d(n-1)
an = -3 + 7(n-1)
an = -3+7n-7
an = 7n-10

  (it says an = 7n-10 if the image doesn't show up)
Note: the n starts at n = 1