Question

Passwords for a certain computer system are strings of uppercase letters. A valid password must contain an even number of X's. Determine a recurrence relation for the number of valid passwords of length n

Answer 1

Of course, 0 is an even number. So we start out with 25 possibilities when n=1. And when n=2 we have 25 squared plus one (for XX). And I think when n=3 we have 25 cubed plus 75. I get how to create the first term (no x's), it's the second (even, non-zero number of x's) I'm having trouble with.