Find an explicit function rule for the sequence - 3, 3, 9, 15, ... Use the formula a (n) = a (1) + (n-1) d and simplify fully.

A (1) = - 3;

a (2) = a (1) + (2 - 1) d;

3 = - 3 + d;

d = 6;

a (3) = a (1) + (3 - 1) d;

9 = - 3 + 2d;

12 = 2d;

d = 6;

a (4) = a (1) + (4 - 1) d;

15 = - 3 + 3d;

18 = 3d;

d = 6;

Then, a (n) = - 3 + (n - 1) 6;

a (n) = - 3 + 6n - 6;

a (n) = 6n - 9 is an explicit functin rule for the sequence - 3, 3, 9, 15, ...