Well, it is correct to write this series as

An = 3n - 5

or

An = An-1 + 3; A1 = -2

The statement that An = 3 An-1 - 5 is just wrong. If that were correct, then given that we know that A1 = -2, then A2 would be 3(-2) - 5 = -11, and A3 would be 3(-11) - 5 = -38, etc.