Let L be a regular language over {a,b}, Suppose a new language defined as follows,
L = x1 , x2, x3, x4,........
L1 = x5, x10, x15 .....
L1 is defined as taking every string which is at positon 5, 10, 15 and so on, in other words, the positions that can be divided by 5.
Is L1 regular?