How many 3-digit numbers are completely divisible 6?

3-digit number divisible by 6 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 t_n = 996.

∴ a + (n - 1)d = 996

⟹ 102 + (n - 1) x 6 = 996

⟹ 6 x (n - 1) = 894

⟹ (n - 1) = 149

⟹ n = 150

∴ Number of terms = 150.