How many 3 digit numbers are divisible by 6 in all?

Required numbers are 102, 108, 114, ... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then,

a + (n - 1)d = 996

  ⟹ 102 + (n - 1) x 6 = 996

  ⟹ 6 x (n - 1) = 894

  ⟹ (n - 1) = 149

  ⟹ n = 150.