A recursive rule written with the formula of: $$a_n = r * a_{n-1}$$ Or as: $$a_n = a_{n-1} + d$$ And an explicit rule written with the formula of: $$a_n = a_1 + (n – 1)d$$ Or as: $$a_n = a_1 * r^{n-1}$$ My math teacher told me that every recursive rule can be written as an explicit rule too and I found that to hold true through all of the math problems I did for homework.